Theorem mtand 654

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 652	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 603  ax-in2 604

This theorem is referenced by:  frirrg  4267  phpm  6752  diffisn  6780  tridc  6786  pm54.43  7039  addcanprleml  7415  addcanprlemu  7416  iseqf1olemklt  10251  pw2dvdseulemle  11834  sqne2sq  11844  ctinfomlemom  11929  ivthinc  12779  pwle2  13182  nninfalllemn  13191