Theorem syl3an132

Description: syl2an with antecedents in standard conjunction form. (Contributed by Alan Sare, 26-Aug-2016)

	Ref	Expression
Hypotheses	syl3an132.1	|- ( ph -> ps )
	syl3an132.2	|- ( ( ch /\ th ) -> ta )
	syl3an132.3	|- ( ( ps /\ ta ) -> et )
Assertion	syl3an132	|- ( ( ph /\ ch /\ th ) -> et )

Proof

Step	Hyp	Ref	Expression
1		syl3an132.1	|- ( ph -> ps )
2		syl3an132.2	|- ( ( ch /\ th ) -> ta )
3		syl3an132.3	|- ( ( ps /\ ta ) -> et )
4	1 2 3	syl2an	|- ( ( ph /\ ( ch /\ th ) ) -> et )
5	4	3impb	|- ( ( ph /\ ch /\ th ) -> et )