Metamath Proof Explorer

Theorem orbi1

Description: Theorem *4.37 of WhiteheadRussell p. 118. (Contributed by NM, 3-Jan-2005)

Ref Expression
Assertion orbi1 ( ( 𝜑 ↔ 𝜓 ) → ( ( 𝜑 ∨ 𝜒 ) ↔ ( 𝜓 ∨ 𝜒 ) ) )

Proof

Step Hyp Ref Expression
1 id ⊢ ( ( 𝜑 ↔ 𝜓 ) → ( 𝜑 ↔ 𝜓 ) )
2 1 orbi1d ⊢ ( ( 𝜑 ↔ 𝜓 ) → ( ( 𝜑 ∨ 𝜒 ) ↔ ( 𝜓 ∨ 𝜒 ) ) )