Theorem biancomd

Description: Commuting conjunction in a biconditional, deduction form. (Contributed by Peter Mazsa, 3-Oct-2018)

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

Proof

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