Theorem syl6bir

Description: A mixed syllogism inference. (Contributed by NM, 18-May-1994)

	Ref	Expression
Hypotheses	syl6bir.1	|- ( ph -> ( ch <-> ps ) )
	syl6bir.2	|- ( ch -> th )
Assertion	syl6bir	|- ( ph -> ( ps -> th ) )

Proof

Step	Hyp	Ref	Expression
1		syl6bir.1	|- ( ph -> ( ch <-> ps ) )
2		syl6bir.2	|- ( ch -> th )
3	1	biimprd	|- ( ph -> ( ps -> ch ) )
4	3 2	syl6	|- ( ph -> ( ps -> th ) )