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  4272  phpm  6759  diffisn  6787  tridc  6793  pm54.43  7046  addcanprleml  7422  addcanprlemu  7423  iseqf1olemklt  10258  pw2dvdseulemle  11845  sqne2sq  11855  ctinfomlemom  11940  ivthinc  12790  pwle2  13193  nninfalllemn  13202