Theorem bi23impib

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

	Ref	Expression
Hypothesis	bi23impib.1	$$⊢\phi \to \left(\left(\psi \wedge \chi \right)\leftrightarrow \theta \right)$$
Assertion	bi23impib	$$⊢\left(\phi \wedge \psi \wedge \chi \right)\to \theta$$

Proof

Step	Hyp	Ref	Expression
1		bi23impib.1	$$⊢\phi \to \left(\left(\psi \wedge \chi \right)\leftrightarrow \theta \right)$$
2	1	biimpd	$$⊢\phi \to \left(\left(\psi \wedge \chi \right)\to \theta \right)$$
3	2	3impib	$$⊢\left(\phi \wedge \psi \wedge \chi \right)\to \theta$$