Theorem mpbid

Description: A deduction from a biconditional, related to modus ponens. (Contributed by NM, 21-Jun-1993)

	Ref	Expression
Hypotheses	mpbid.min	|- ( ph -> ps )
	mpbid.maj	|- ( ph -> ( ps <-> ch ) )
Assertion	mpbid	|- ( ph -> ch )

Proof

Step	Hyp	Ref	Expression
1		mpbid.min	|- ( ph -> ps )
2		mpbid.maj	|- ( ph -> ( ps <-> ch ) )
3	2	biimpd	|- ( ph -> ( ps -> ch ) )
4	1 3	mpd	|- ( ph -> ch )