Theorem mpbidi

Description: A deduction from a biconditional, related to modus ponens. (Contributed by NM, 9-Aug-1994)

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

Proof

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