Theorem mt2 170

Description: A rule similar to modus tollens. (Contributed by NM, 19-Aug-1993.) (Proof shortened by Wolf Lammen, 10-Sep-2013.)

Hypotheses

Ref	Expression
mt2.1	⊢ ψ
mt2.2	⊢ (φ → ¬ ψ)

Assertion

Ref	Expression
mt2	⊢ ¬ φ

Proof of Theorem mt2

Step	Hyp	Ref	Expression
1		mt2.1	. . 3 ⊢ ψ
2	1	a1i 10	. 2 ⊢ (φ → ψ)
3		mt2.2	. 2 ⊢ (φ → ¬ ψ)
4	2, 3	pm2.65i 165	1 ⊢ ¬ φ

Syntax hints:  ¬ wn 3   → wi 4

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem is referenced by:  bijust  175  19.2OLD  1700  ax9dgen  1716  nnsucelr  4429  ssfin  4471