Theorem syl2an3an

Description: syl3an with antecedents in standard conjunction form. (Contributed by Alan Sare, 31-Aug-2016)

	Ref	Expression
Hypotheses	syl2an3an.1	|- ( ph -> ps )
	syl2an3an.2	|- ( ph -> ch )
	syl2an3an.3	|- ( th -> ta )
	syl2an3an.4	|- ( ( ps /\ ch /\ ta ) -> et )
Assertion	syl2an3an	|- ( ( ph /\ th ) -> et )

Proof

Step	Hyp	Ref	Expression
1		syl2an3an.1	|- ( ph -> ps )
2		syl2an3an.2	|- ( ph -> ch )
3		syl2an3an.3	|- ( th -> ta )
4		syl2an3an.4	|- ( ( ps /\ ch /\ ta ) -> et )
5	1 2 3 4	syl3an	|- ( ( ph /\ ph /\ th ) -> et )
6	5	3anidm12	|- ( ( ph /\ th ) -> et )