Theorem bi3impa

Description: Similar to 3impa with implication in hypothesis replaced by biconditional. (Contributed by Alan Sare, 6-Nov-2017)

	Ref	Expression
Hypothesis	bi3impa.1	$$⊢\left(\left(\phi \wedge \psi \right)\wedge \chi \right)\leftrightarrow \theta$$
Assertion	bi3impa	$$⊢\left(\phi \wedge \psi \wedge \chi \right)\to \theta$$

Proof

Step	Hyp	Ref	Expression
1		bi3impa.1	$$⊢\left(\left(\phi \wedge \psi \right)\wedge \chi \right)\leftrightarrow \theta$$
2	1	biimpi	$$⊢\left(\left(\phi \wedge \psi \right)\wedge \chi \right)\to \theta$$
3	2	3impa	$$⊢\left(\phi \wedge \psi \wedge \chi \right)\to \theta$$