Theorem sylanblc

Description: Syllogism inference combined with a biconditional. (Contributed by BJ, 25-Apr-2019)

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

Proof

Step	Hyp	Ref	Expression
1		sylanblc.1	|- ( ph -> ps )
2		sylanblc.2	|- ch
3		sylanblc.3	|- ( ( ps /\ ch ) <-> th )
4	3	biimpi	|- ( ( ps /\ ch ) -> th )
5	1 2 4	sylancl	|- ( ph -> th )