Theorem mt4 129

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

Hypotheses

Ref	Expression
mt4.1	|- ph
mt4.2	|- (-. ps -> -. ph)

Assertion

Ref	Expression
mt4	|- ps

Proof of Theorem mt4

Step	Hyp	Ref	Expression
1		mt4.1	. 2 |- ph
2		mt4.2	. . 3 |- (-. ps -> -. ph)
3	2	con4i 122	. 2 |- (ph -> ps)
4	1, 3	ax-mp 5	1 |- ps

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)