Theorem mtord 795

Description: A modus tollens deduction involving disjunction. (Contributed by Jeff Hankins, 15-Jul-2009.) (Revised by Mario Carneiro, 31-Jan-2015.)

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.3	. . 3 |- ( ph -> ( ps -> ( ch \/ th ) ) )
2		mtord.1	. . . . 5 |- ( ph -> -. ch )
3	2	pm2.21d 628	. . . 4 |- ( ph -> ( ch -> -. ps ) )
4		mtord.2	. . . . 5 |- ( ph -> -. th )
5	4	pm2.21d 628	. . . 4 |- ( ph -> ( th -> -. ps ) )
6	3, 5	jaod 729	. . 3 |- ( ph -> ( ( ch \/ th ) -> -. ps ) )
7	1, 6	syld 45	. 2 |- ( ph -> ( ps -> -. ps ) )
8	7	pm2.01d 627	1 |- ( ph -> -. ps )

This proof depends on syntax axioms:   -. wn 3   -> wi 4   \/ wo 720

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in1 623  ax-in2 624  ax-io 721

This proof depends on definitions:  df-bi 117

This theorem is used by:  swoer  6835