Theorem baibr

Description: Move conjunction outside of biconditional. (Contributed by NM, 11-Jul-1994)

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

Proof

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