Theorem syl3c

Description: A syllogism inference combined with contraction. (Contributed by Alan Sare, 7-Jul-2011)

	Ref	Expression
Hypotheses	syl3c.1	|- ( ph -> ps )
	syl3c.2	|- ( ph -> ch )
	syl3c.3	|- ( ph -> th )
	syl3c.4	|- ( ps -> ( ch -> ( th -> ta ) ) )
Assertion	syl3c	|- ( ph -> ta )

Proof

Step	Hyp	Ref	Expression
1		syl3c.1	|- ( ph -> ps )
2		syl3c.2	|- ( ph -> ch )
3		syl3c.3	|- ( ph -> th )
4		syl3c.4	|- ( ps -> ( ch -> ( th -> ta ) ) )
5	1 2 4	sylc	|- ( ph -> ( th -> ta ) )
6	3 5	mpd	|- ( ph -> ta )