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 ) ) )