Theorem bianim

Description: Exchanging conjunction in a biconditional. (Contributed by Peter Mazsa, 31-Jul-2023)

	Ref	Expression
Hypotheses	bianim.1	$$⊢\phi \leftrightarrow \left(\psi \wedge \chi \right)$$
	bianim.2	$$⊢\chi \to \left(\psi \leftrightarrow \theta \right)$$
Assertion	bianim	$$⊢\phi \leftrightarrow \left(\theta \wedge \chi \right)$$

Proof

Step	Hyp	Ref	Expression
1		bianim.1	$$⊢\phi \leftrightarrow \left(\psi \wedge \chi \right)$$
2		bianim.2	$$⊢\chi \to \left(\psi \leftrightarrow \theta \right)$$
3	2	pm5.32ri	$$⊢\left(\psi \wedge \chi \right)\leftrightarrow \left(\theta \wedge \chi \right)$$
4	1 3	bitri	$$⊢\phi \leftrightarrow \left(\theta \wedge \chi \right)$$