Theorem mpbiran2d

Description: Detach truth from conjunction in biconditional. Deduction form. (Contributed by Peter Mazsa, 24-Sep-2022)

	Ref	Expression
Hypotheses	mpbiran2d.1	$$⊢\phi \to \theta$$
	mpbiran2d.2	$$⊢\phi \to \left(\psi \leftrightarrow \left(\chi \wedge \theta \right)\right)$$
Assertion	mpbiran2d	$$⊢\phi \to \left(\psi \leftrightarrow \chi \right)$$

Proof

Step	Hyp	Ref	Expression
1		mpbiran2d.1	$$⊢\phi \to \theta$$
2		mpbiran2d.2	$$⊢\phi \to \left(\psi \leftrightarrow \left(\chi \wedge \theta \right)\right)$$
3	2	biancomd	$$⊢\phi \to \left(\psi \leftrightarrow \left(\theta \wedge \chi \right)\right)$$
4	1 3	mpbirand	$$⊢\phi \to \left(\psi \leftrightarrow \chi \right)$$