Theorem bi13imp23

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

	Ref	Expression
Hypothesis	bi13imp23.1	$$⊢\phi \leftrightarrow \left(\psi \to \left(\chi \to \theta \right)\right)$$
Assertion	bi13imp23	$$⊢\left(\phi \wedge \psi \wedge \chi \right)\to \theta$$

Proof

Step	Hyp	Ref	Expression
1		bi13imp23.1	$$⊢\phi \leftrightarrow \left(\psi \to \left(\chi \to \theta \right)\right)$$
2	1	biimpi	$$⊢\phi \to \left(\psi \to \left(\chi \to \theta \right)\right)$$
3	2	3imp	$$⊢\left(\phi \wedge \psi \wedge \chi \right)\to \theta$$