Theorem mt3 171

Description: A rule similar to modus tollens. (Contributed by NM, 18-May-1994.) (Proof shortened by Wolf Lammen, 11-Sep-2013.)

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	. . 3 ⊢ ¬ ψ
2		mt3.2	. . 3 ⊢ (¬ φ → ψ)
3	1, 2	mto 167	. 2 ⊢ ¬ ¬ φ
4	3	notnotri 106	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:  equidOLD  1677  spOLD  1748  spimehOLD  1821  cbv3hvOLD  1851  ax9  1949  equidq  2175