Theorem bi13imp2

Description: Similar to 3imp except the outermost and innermost implications are biconditionals. (Contributed by Alan Sare, 6-Nov-2017)

	Ref	Expression
Hypothesis	bi13imp2.1	$$⊢\phi \leftrightarrow \left(\psi \to \left(\chi \leftrightarrow \theta \right)\right)$$
Assertion	bi13imp2	$$⊢\left(\phi \wedge \psi \wedge \chi \right)\to \theta$$

Proof

Step	Hyp	Ref	Expression
1		bi13imp2.1	$$⊢\phi \leftrightarrow \left(\psi \to \left(\chi \leftrightarrow \theta \right)\right)$$
2	1	biimpi	$$⊢\phi \to \left(\psi \to \left(\chi \leftrightarrow \theta \right)\right)$$
3	2	bi33imp12	$$⊢\left(\phi \wedge \psi \wedge \chi \right)\to \theta$$