Theorem bibi12i

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

	Ref	Expression
Hypotheses	bibi2i.1	⊢ ( 𝜑 ↔ 𝜓 )
	bibi12i.2	⊢ ( 𝜒 ↔ 𝜃 )
Assertion	bibi12i	⊢ ( ( 𝜑 ↔ 𝜒 ) ↔ ( 𝜓 ↔ 𝜃 ) )

Proof

Step	Hyp	Ref	Expression
1		bibi2i.1	⊢ ( 𝜑 ↔ 𝜓 )
2		bibi12i.2	⊢ ( 𝜒 ↔ 𝜃 )
3	2	bibi2i	⊢ ( ( 𝜑 ↔ 𝜒 ) ↔ ( 𝜑 ↔ 𝜃 ) )
4	1	bibi1i	⊢ ( ( 𝜑 ↔ 𝜃 ) ↔ ( 𝜓 ↔ 𝜃 ) )
5	3 4	bitri	⊢ ( ( 𝜑 ↔ 𝜒 ) ↔ ( 𝜓 ↔ 𝜃 ) )