Theorem bi23imp1

Description: Similar to 3imp except all but outermost implication are biconditionals. (Contributed by Alan Sare, 6-Nov-2017)

	Ref	Expression
Hypothesis	bi23imp1.1	$$⊢\phi \to \left(\psi \leftrightarrow \left(\chi \leftrightarrow \theta \right)\right)$$
Assertion	bi23imp1	$$⊢\left(\phi \wedge \psi \wedge \chi \right)\to \theta$$

Proof

Step	Hyp	Ref	Expression
1		bi23imp1.1	$$⊢\phi \to \left(\psi \leftrightarrow \left(\chi \leftrightarrow \theta \right)\right)$$
2		biimp	$$⊢\left(\chi \leftrightarrow \theta \right)\to \left(\chi \to \theta \right)$$
3	1 2	syl6bi	$$⊢\phi \to \left(\psi \to \left(\chi \to \theta \right)\right)$$
4	3	3imp	$$⊢\left(\phi \wedge \psi \wedge \chi \right)\to \theta$$