Theorem anbi12i

Description: Conjoin both sides of two equivalences. (Contributed by NM, 12-Mar-1993)

	Ref	Expression
Hypotheses	anbi12.1	$$⊢\phi \leftrightarrow \psi$$
	anbi12.2	$$⊢\chi \leftrightarrow \theta$$
Assertion	anbi12i	$$⊢\left(\phi \wedge \chi \right)\leftrightarrow \left(\psi \wedge \theta \right)$$

Proof

Step	Hyp	Ref	Expression
1		anbi12.1	$$⊢\phi \leftrightarrow \psi$$
2		anbi12.2	$$⊢\chi \leftrightarrow \theta$$
3	1	anbi1i	$$⊢\left(\phi \wedge \chi \right)\leftrightarrow \left(\psi \wedge \chi \right)$$
4	2	anbi2i	$$⊢\left(\psi \wedge \chi \right)\leftrightarrow \left(\psi \wedge \theta \right)$$
5	3 4	bitri	$$⊢\left(\phi \wedge \chi \right)\leftrightarrow \left(\psi \wedge \theta \right)$$