Deduction theorem

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Conversion from proof using the deduction meta-theorem to axiomatic proof

Axiom schemas Begging the question Tautologies Curry–Howard correspondence Meta-theorem

7 related topics

Overview

Mathematical logic Metatheorem Conditional proofs Propositional logic First-order logic

16 related topics

The deduction theorem in predicate logic

Theory Closed Modus ponens Rule of inference Generalization

6 related topics

Helpful theorems

Peirce's law

1 related topics

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Overview

Mathematical logic
Metatheorem
Conditional proofs Conditional proof
Propositional logic
First-order logic
Hilbert-style deduction systems Hilbert-style deduction system
Natural deduction
Implication introduction
Empty set
Closed formula Sentence (mathematical logic)
Birkhoff Garrett Birkhoff
Von Neumann John von Neumann
Quantum logic
Linear subspaces Linear subspace
Hilbert space
Non-distributive lattice Distributive lattice

Conversion from proof using the deduction meta-theorem to axiomatic proof

Helpful theorems

Peirce's law

The deduction theorem in predicate logic

Theory Theory (mathematical logic)
Closed Well-formed formula
Modus ponens
Rule of inference
Generalization Generalization (logic)
Free variables Free variables and bound variables

Example of conversion

Lambda elimination

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Avg. degree1.95

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Deduction theorem

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related to References · 58

Deduction theorem → An, Applied, Berlin, Business Media, Carl, Concise Introduction, Curtis, Dover Publications, Fitch, Franks, Frederic Brenton, Hewitt, IEEE Internet Computing, Introduction, ISBN, Joseph, July, Kleene, Kohlenbach, LCCN

related to External links · 5

Deduction theorem → Introduction, Karlis Podnieks, Mathematical Logic, See Section, Vilnis Detlovs

related to Proof of the deduction theorem · 4

Deduction theorem → Delta, Hilbert-style, Let, We

is a · 2

Deduction theorem → important tool in Hilbert-style deduction systems because it permits one to write more comprehensible and usually much shorter proofs than would be possible without it, metatheorem that justifies doing conditional proofs from a hypothesis in systems that do not explicitly axiomatize that hypothesis

related to The deduction theorem in predicate logic · 2

Deduction theorem → If, The

related to Helpful theorems · 1

Deduction theorem → If

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deduction modus ponens theorem axiom logic hypothesis displaystyle proof one delta vdash step cup prove systems qed propositional using inference

Entity relationships Subject–Predicate–Object triples

Subject	Predicate	Object	Confidence	Src
Deduction theorem	is a	metatheorem that justifies doing conditional proofs from a hypothesis in systems that do not explicitly axiomatize that hypothesis	0.90	text
Deduction theorem	is a	important tool in Hilbert-style deduction systems because it permits one to write more comprehensible and usually much shorter proofs than would be possible without it	0.90	text
Deduction theorem	related to External links	Introduction	0.60	section
Deduction theorem	related to External links	Mathematical Logic	0.60	section
Deduction theorem	related to External links	Vilnis Detlovs	0.60	section
Deduction theorem	related to External links	Karlis Podnieks	0.60	section
Deduction theorem	related to External links	See Section	0.60	section
Deduction theorem	related to Helpful theorems	If	0.60	section
Deduction theorem	related to Proof of the deduction theorem	We	0.60	section
Deduction theorem	related to Proof of the deduction theorem	Hilbert-style	0.60	section
Deduction theorem	related to Proof of the deduction theorem	Let	0.60	section
Deduction theorem	related to Proof of the deduction theorem	Delta	0.60	section

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Conversion from proof using the deduction meta-theorem to axiomatic proof

Overview

The deduction theorem in predicate logic

Helpful theorems

Key facts & relationships

Topics to explore

Overview

Conversion from proof using the deduction meta-theorem to axiomatic proof

Helpful theorems

The deduction theorem in predicate logic

Example of conversion

Advanced semantic analysis

Map overview Semantic statistics

Deduction theorem

How this topic connects Entity context

Deduction theorem

Top relations

Important terminology Word statistics

Important terminology

Entity relationships Subject–Predicate–Object triples

Related concept clusters Concept neighborhoods

Connections between topic areas Semantic bridges