Theorem syl2imc

Description: A commuted version of syl2im . Implication-only version of syl2anr . (Contributed by BJ, 20-Oct-2021)

	Ref	Expression
Hypotheses	syl2im.1	|- ( ph -> ps )
	syl2im.2	|- ( ch -> th )
	syl2im.3	|- ( ps -> ( th -> ta ) )
Assertion	syl2imc	|- ( ch -> ( ph -> ta ) )

Proof

Step	Hyp	Ref	Expression
1		syl2im.1	|- ( ph -> ps )
2		syl2im.2	|- ( ch -> th )
3		syl2im.3	|- ( ps -> ( th -> ta ) )
4	1 2 3	syl2im	|- ( ph -> ( ch -> ta ) )
5	4	com12	|- ( ch -> ( ph -> ta ) )