Theorem bi12imp3

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

	Ref	Expression
Hypothesis	bi12imp3.1	$$⊢\phi \leftrightarrow \left(\psi \leftrightarrow \left(\chi \to \theta \right)\right)$$
Assertion	bi12imp3	$$⊢\left(\phi \wedge \psi \wedge \chi \right)\to \theta$$

Proof

Step	Hyp	Ref	Expression
1		bi12imp3.1	$$⊢\phi \leftrightarrow \left(\psi \leftrightarrow \left(\chi \to \theta \right)\right)$$
2	1	biimpi	$$⊢\phi \to \left(\psi \leftrightarrow \left(\chi \to \theta \right)\right)$$
3	2	bi23imp13	$$⊢\left(\phi \wedge \psi \wedge \chi \right)\to \theta$$