Theorem bibi12i

Description: The equivalence of two equivalences. (Contributed by NM, 26-May-1993)

	Ref	Expression
Hypotheses	bibi2i.1	$$⊢\phi \leftrightarrow \psi$$
	bibi12i.2	$$⊢\chi \leftrightarrow \theta$$
Assertion	bibi12i	$$⊢\left(\phi \leftrightarrow \chi \right)\leftrightarrow \left(\psi \leftrightarrow \theta \right)$$

Proof

Step	Hyp	Ref	Expression
1		bibi2i.1	$$⊢\phi \leftrightarrow \psi$$
2		bibi12i.2	$$⊢\chi \leftrightarrow \theta$$
3	2	bibi2i	$$⊢\left(\phi \leftrightarrow \chi \right)\leftrightarrow \left(\phi \leftrightarrow \theta \right)$$
4	1	bibi1i	$$⊢\left(\phi \leftrightarrow \theta \right)\leftrightarrow \left(\psi \leftrightarrow \theta \right)$$
5	3 4	bitri	$$⊢\left(\phi \leftrightarrow \chi \right)\leftrightarrow \left(\psi \leftrightarrow \theta \right)$$