Theorem biimp3a

Description: Infer implication from a logical equivalence. Similar to biimpa . (Contributed by NM, 4-Sep-2005)

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

Proof

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