Theorem mtord 641

Description: A modus tollens deduction involving disjunction. (Contributed by Jeff Hankins, 15-Jul-2009.)

Hypotheses

Ref	Expression
mtord.1	|- (ph -> -. ch)
mtord.2	|- (ph -> -. th)
mtord.3	|- (ph -> (ps -> (ch \/ th)))

Assertion

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

Proof of Theorem mtord

Step	Hyp	Ref	Expression
1		mtord.2	. 2 |- (ph -> -. th)
2		mtord.1	. . 3 |- (ph -> -. ch)
3		mtord.3	. . . 4 |- (ph -> (ps -> (ch \/ th)))
4		df-or 359	. . . 4 |- ((ch \/ th) <-> (-. ch -> th))
5	3, 4	syl6ib 217	. . 3 |- (ph -> (ps -> (-. ch -> th)))
6	2, 5	mpid 37	. 2 |- (ph -> (ps -> th))
7	1, 6	mtod 168	1 |- (ph -> -. ps)

Syntax hints:  -. wn 3   -> wi 4   \/ wo 357

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-or 359

This theorem is referenced by: (None)