Theorem rbaib

Description: Move conjunction outside of biconditional. (Contributed by Mario Carneiro, 11-Sep-2015) (Proof shortened by Wolf Lammen, 19-Jan-2020)

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

Proof

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