Theorem logic1a

Description: Variant of logic1 . (Contributed by Zhi Wang, 30-Aug-2024)

	Ref	Expression
Hypotheses	logic1.1	$$⊢\phi \to \left(\psi \leftrightarrow \chi \right)$$
	logic1a.2	$$⊢\left(\phi \wedge \psi \right)\to \left(\theta \leftrightarrow \tau \right)$$
Assertion	logic1a	$$⊢\phi \to \left(\left(\psi \to \theta \right)\leftrightarrow \left(\chi \to \tau \right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		logic1.1	$$⊢\phi \to \left(\psi \leftrightarrow \chi \right)$$
2		logic1a.2	$$⊢\left(\phi \wedge \psi \right)\to \left(\theta \leftrightarrow \tau \right)$$
3	2	ex	$$⊢\phi \to \left(\psi \to \left(\theta \leftrightarrow \tau \right)\right)$$
4	1 3	logic1	$$⊢\phi \to \left(\left(\psi \to \theta \right)\leftrightarrow \left(\chi \to \tau \right)\right)$$