Theorem biimp3ar

Description: Infer implication from a logical equivalence. Similar to biimpar . (Contributed by NM, 2-Jan-2009)

	Ref	Expression
Hypothesis	biimp3a.1	$$⊢\left(\phi \wedge \psi \right)\to \left(\chi \leftrightarrow \theta \right)$$
Assertion	biimp3ar	$$⊢\left(\phi \wedge \psi \wedge \theta \right)\to \chi$$

Proof

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