Theorem bianabs

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

	Ref	Expression
Hypothesis	bianabs.1	$$⊢\phi \to \left(\psi \leftrightarrow \left(\phi \wedge \chi \right)\right)$$
Assertion	bianabs	$$⊢\phi \to \left(\psi \leftrightarrow \chi \right)$$

Proof

Step	Hyp	Ref	Expression
1		bianabs.1	$$⊢\phi \to \left(\psi \leftrightarrow \left(\phi \wedge \chi \right)\right)$$
2		ibar	$$⊢\phi \to \left(\chi \leftrightarrow \left(\phi \wedge \chi \right)\right)$$
3	1 2	bitr4d	$$⊢\phi \to \left(\psi \leftrightarrow \chi \right)$$