Theorem anbi1cd

Description: Introduce a proposition as left conjunct on the left-hand side and right conjunct on the right-hand side of an equivalence. Deduction form. (Contributed by Peter Mazsa, 22-May-2021)

	Ref	Expression
Hypothesis	anbi1cd.1	$$⊢\phi \to \left(\psi \leftrightarrow \chi \right)$$
Assertion	anbi1cd	$$⊢\phi \to \left(\left(\theta \wedge \psi \right)\leftrightarrow \left(\chi \wedge \theta \right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		anbi1cd.1	$$⊢\phi \to \left(\psi \leftrightarrow \chi \right)$$
2	1	anbi2d	$$⊢\phi \to \left(\left(\theta \wedge \psi \right)\leftrightarrow \left(\theta \wedge \chi \right)\right)$$
3	2	biancomd	$$⊢\phi \to \left(\left(\theta \wedge \psi \right)\leftrightarrow \left(\chi \wedge \theta \right)\right)$$