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Metamath Proof Explorer

Theorem abai

Description: Introduce one conjunct as an antecedent to the other. "abai" stands for "and, biconditional, and, implication". (Contributed by NM, 12-Aug-1993) (Proof shortened by Wolf Lammen, 7-Dec-2012)

		Ref	Expression
	Assertion	abai	\|- ( ( ph /\ ps ) <-> ( ph /\ ( ph -> ps ) ) )

Proof

Step	Hyp	Ref	Expression
1		biimt	\|- ( ph -> ( ps <-> ( ph -> ps ) ) )
2	1	pm5.32i	\|- ( ( ph /\ ps ) <-> ( ph /\ ( ph -> ps ) ) )