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Metamath Proof Explorer

Theorem bianabs

Description: Absorb a hypothesis into the second member of a biconditional. (Contributed by FL, 15-Feb-2007)

		Ref	Expression
	Hypothesis	bianabs.1	$⊢ φ \to (ψ \leftrightarrow (φ \land χ))$
	Assertion	bianabs	$⊢ φ \to (ψ \leftrightarrow χ)$

Step	Hyp	Ref	Expression
1		bianabs.1	$⊢ φ \to (ψ \leftrightarrow (φ \land χ))$
2		ibar	$⊢ φ \to (χ \leftrightarrow (φ \land χ))$
3	1 2	bitr4d	$⊢ φ \to (ψ \leftrightarrow χ)$