Theorem syl8ib

Description: A syllogism rule of inference. The second premise is used to replace the consequent of the first premise. (Contributed by NM, 1-Aug-1994)

	Ref	Expression
Hypotheses	syl8ib.1	|- ( ph -> ( ps -> ( ch -> th ) ) )
	syl8ib.2	|- ( th <-> ta )
Assertion	syl8ib	|- ( ph -> ( ps -> ( ch -> ta ) ) )

Proof

Step	Hyp	Ref	Expression
1		syl8ib.1	|- ( ph -> ( ps -> ( ch -> th ) ) )
2		syl8ib.2	|- ( th <-> ta )
3	2	biimpi	|- ( th -> ta )
4	1 3	syl8	|- ( ph -> ( ps -> ( ch -> ta ) ) )