Theorem orbi12i

Description: Infer the disjunction of two equivalences. (Contributed by NM, 3-Jan-1993)

	Ref	Expression
Hypotheses	orbi12i.1	⊢ ( 𝜑 ↔ 𝜓 )
	orbi12i.2	⊢ ( 𝜒 ↔ 𝜃 )
Assertion	orbi12i	⊢ ( ( 𝜑 ∨ 𝜒 ) ↔ ( 𝜓 ∨ 𝜃 ) )

Proof

Step	Hyp	Ref	Expression
1		orbi12i.1	⊢ ( 𝜑 ↔ 𝜓 )
2		orbi12i.2	⊢ ( 𝜒 ↔ 𝜃 )
3	2	orbi2i	⊢ ( ( 𝜑 ∨ 𝜒 ) ↔ ( 𝜑 ∨ 𝜃 ) )
4	1	orbi1i	⊢ ( ( 𝜑 ∨ 𝜃 ) ↔ ( 𝜓 ∨ 𝜃 ) )
5	3 4	bitri	⊢ ( ( 𝜑 ∨ 𝜒 ) ↔ ( 𝜓 ∨ 𝜃 ) )