Theorem bi33imp12

Description: 3imp with innermost implication of the hypothesis a biconditional. (Contributed by Alan Sare, 6-Nov-2017)

	Ref	Expression
Hypothesis	bi33imp12.1	$$⊢\phi \to \left(\psi \to \left(\chi \leftrightarrow \theta \right)\right)$$
Assertion	bi33imp12	$$⊢\left(\phi \wedge \psi \wedge \chi \right)\to \theta$$

Proof

Step	Hyp	Ref	Expression
1		bi33imp12.1	$$⊢\phi \to \left(\psi \to \left(\chi \leftrightarrow \theta \right)\right)$$
2		biimp	$$⊢\left(\chi \leftrightarrow \theta \right)\to \left(\chi \to \theta \right)$$
3	1 2	syl6	$$⊢\phi \to \left(\psi \to \left(\chi \to \theta \right)\right)$$
4	3	3imp	$$⊢\left(\phi \wedge \psi \wedge \chi \right)\to \theta$$