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Metamath Proof Explorer

Theorem orbi1r

Description: orbi1 with order of disjuncts reversed. Derived from orbi1rVD . (Contributed by Alan Sare, 31-Dec-2011) (Proof modification is discouraged.) (New usage is discouraged.)

		Ref	Expression
	Assertion	orbi1r	⊢ ( ( 𝜑 ↔ 𝜓 ) → ( ( 𝜒 ∨ 𝜑 ) ↔ ( 𝜒 ∨ 𝜓 ) ) )

Proof

Step	Hyp	Ref	Expression
1		id	⊢ ( ( 𝜑 ↔ 𝜓 ) → ( 𝜑 ↔ 𝜓 ) )
2	1	orbi2d	⊢ ( ( 𝜑 ↔ 𝜓 ) → ( ( 𝜒 ∨ 𝜑 ) ↔ ( 𝜒 ∨ 𝜓 ) ) )