Theorem mt4 129

Description: The rule of modus tollens. (Contributed by Wolf Lammen, 12-May-2013.)

Hypotheses

Ref	Expression
mt4.1	⊢ φ
mt4.2	⊢ (¬ ψ → ¬ φ)

Assertion

Ref	Expression
mt4	⊢ ψ

Proof of Theorem mt4

Step	Hyp	Ref	Expression
1		mt4.1	. 2 ⊢ φ
2		mt4.2	. . 3 ⊢ (¬ ψ → ¬ φ)
3	2	con4i 122	. 2 ⊢ (φ → ψ)
4	1, 3	ax-mp 5	1 ⊢ ψ

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: (None)