Theorem mtand 640

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 423	. 2 |- (ph -> (ps -> ch))
4	1, 3	mtod 168	1 |- (ph -> -. ps)

Syntax hints:  -. wn 3   -> wi 4   /\ wa 358

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 177  df-an 360

This theorem is referenced by:  tfinnn  4535  sfin111  4537  nchoicelem5  6294