Theorem mtand 655

Description: A modus tollens deduction. (Contributed by Jeff Hankins, 19-Aug-2009.)

Hypotheses

Ref	Expression
mtand.1	|- ( ph -> -. ch )
mtand.2	|- ( ( ph /\ ps ) -> ch )

Assertion

Ref	Expression
mtand	|- ( ph -> -. ps )

Proof of Theorem mtand

Step	Hyp	Ref	Expression
1		mtand.1	. 2 |- ( ph -> -. ch )
2		mtand.2	. . 3 |- ( ( ph /\ ps ) -> ch )
3	2	ex 114	. 2 |- ( ph -> ( ps -> ch ) )
4	1, 3	mtod 653	1 |- ( ph -> -. ps )

Syntax hints:   -. wn 3   -> wi 4   /\ wa 103

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia3 107  ax-in1 604  ax-in2 605

This theorem is referenced by:  frirrg  4280  phpm  6767  diffisn  6795  tridc  6801  pm54.43  7063  addcanprleml  7446  addcanprlemu  7447  iseqf1olemklt  10289  pw2dvdseulemle  11881  sqne2sq  11891  ctinfomlemom  11976  ivthinc  12829  pwle2  13366  nninfalllemn  13377