Theorem rbaibd

Description: Move conjunction outside of biconditional. (Contributed by Mario Carneiro, 11-Sep-2015)

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

Proof

Step	Hyp	Ref	Expression
1		baibd.1	$$⊢\phi \to \left(\psi \leftrightarrow \left(\chi \wedge \theta \right)\right)$$
2	1	biancomd	$$⊢\phi \to \left(\psi \leftrightarrow \left(\theta \wedge \chi \right)\right)$$
3	2	baibd	$$⊢\left(\phi \wedge \theta \right)\to \left(\psi \leftrightarrow \chi \right)$$