Theorem bi123impia

Description: 3impia with the implications of the hypothesis biconditionals. (Contributed by Alan Sare, 6-Nov-2017)

	Ref	Expression
Hypothesis	bi123impia.1	$$⊢\left(\phi \wedge \psi \right)\leftrightarrow \left(\chi \leftrightarrow \theta \right)$$
Assertion	bi123impia	$$⊢\left(\phi \wedge \psi \wedge \chi \right)\to \theta$$

Proof

Step	Hyp	Ref	Expression
1		bi123impia.1	$$⊢\left(\phi \wedge \psi \right)\leftrightarrow \left(\chi \leftrightarrow \theta \right)$$
2	1	biimpi	$$⊢\left(\phi \wedge \psi \right)\to \left(\chi \leftrightarrow \theta \right)$$
3	2	biimp3a	$$⊢\left(\phi \wedge \psi \wedge \chi \right)\to \theta$$