Theorem mt3 99

Description: A rule similar to modus tollens.

Hypotheses

Ref	Expression
mt3.1	⊢ ¬ ψ
mt3.2	⊢ (¬ φ → ψ)

Assertion

Ref	Expression
mt3	⊢ φ

Proof of Theorem mt3

Step	Hyp	Ref	Expression
1		mt3.1	. 2 ⊢ ¬ ψ
2		mt3.2	. . 3 ⊢ (¬ φ → ψ)
3	2	con1i 88	. 2 ⊢ (¬ ψ → φ)
4	1, 3	ax-mp 6	1 ⊢ φ

Syntax hints:  ¬ wn 1   → wi 2

This theorem is referenced by:  omelon 3476  hatomistic 5755

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6

metamath.org