Theorem syl2im

Description: Replace two antecedents. Implication-only version of syl2an . (Contributed by Wolf Lammen, 14-May-2013)

	Ref	Expression
Hypotheses	syl2im.1	|- ( ph -> ps )
	syl2im.2	|- ( ch -> th )
	syl2im.3	|- ( ps -> ( th -> ta ) )
Assertion	syl2im	|- ( ph -> ( ch -> ta ) )

Proof

Step	Hyp	Ref	Expression
1		syl2im.1	|- ( ph -> ps )
2		syl2im.2	|- ( ch -> th )
3		syl2im.3	|- ( ps -> ( th -> ta ) )
4	2 3	syl5	|- ( ps -> ( ch -> ta ) )
5	1 4	syl	|- ( ph -> ( ch -> ta ) )