Theorem mtand 623

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 113	. 2 |- ( ph -> ( ps -> ch ) )
4	1, 3	mtod 621	1 |- ( ph -> -. ps )

Syntax hints:   -. wn 3   -> wi 4   /\ wa 102

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia3 106  ax-in1 576  ax-in2 577

This theorem is referenced by:  frirrg  4105  phpm  6351  diffisn  6377  pm54.43  6459  addcanprleml  6804  addcanprlemu  6805  pw2dvdseulemle  10545  sqne2sq  10555