Theorem syl2anc2

Description: Double syllogism inference combined with contraction. (Contributed by BTernaryTau, 29-Sep-2023)

	Ref	Expression
Hypotheses	syl2anc2.1	|- ( ph -> ps )
	syl2anc2.2	|- ( ps -> ch )
	syl2anc2.3	|- ( ( ps /\ ch ) -> th )
Assertion	syl2anc2	|- ( ph -> th )

Proof

Step	Hyp	Ref	Expression
1		syl2anc2.1	|- ( ph -> ps )
2		syl2anc2.2	|- ( ps -> ch )
3		syl2anc2.3	|- ( ( ps /\ ch ) -> th )
4	1 2	syl	|- ( ph -> ch )
5	1 4 3	syl2anc	|- ( ph -> th )