Theorem mtord 692

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 385	. . . 4 |- ( ( ch \/ th ) <-> ( -. ch -> th ) )
5	3, 4	syl6ib 241	. . 3 |- ( ph -> ( ps -> ( -. ch -> th ) ) )
6	2, 5	mpid 44	. 2 |- ( ph -> ( ps -> th ) )
7	1, 6	mtod 189	1 |- ( ph -> -. ps )

Syntax hints:   -. wn 3   -> wi 4   \/ wo 383

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 197  df-or 385

This theorem is referenced by:  swoer  7772  inar1  9597