Theorem mtord

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

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

Proof

Step	Hyp	Ref	Expression
1		mtord.1	|- ( ph -> -. ch )
2		mtord.2	|- ( ph -> -. th )
3		mtord.3	|- ( ph -> ( ps -> ( ch \/ th ) ) )
4		pm2.53	|- ( ( ch \/ th ) -> ( -. ch -> th ) )
5	3 1 4	syl6ci	|- ( ph -> ( ps -> th ) )
6	2 5	mtod	|- ( ph -> -. ps )