Theorem mpbird

Description: A deduction from a biconditional, related to modus ponens. (Contributed by NM, 5-Aug-1993)

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

Proof

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