Theorem baib

Description: Move conjunction outside of biconditional. (Contributed by NM, 13-May-1999)

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

Proof

Step	Hyp	Ref	Expression
1		baib.1	$$⊢\phi \leftrightarrow \left(\psi \wedge \chi \right)$$
2		ibar	$$⊢\psi \to \left(\chi \leftrightarrow \left(\psi \wedge \chi \right)\right)$$
3	1 2	bitr4id	$$⊢\psi \to \left(\phi \leftrightarrow \chi \right)$$