Theorem orbi1 931

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

Assertion

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

Proof of Theorem orbi1

Step	Hyp	Ref	Expression
1		id 23	. 2 ⊢ ((𝜑 ↔ 𝜓) → (𝜑 ↔ 𝜓))
2	1	orbi1d 930	1 ⊢ ((𝜑 ↔ 𝜓) → ((𝜑 ∨ 𝜒) ↔ (𝜓 ∨ 𝜒)))

This proof depends on syntax axioms:   → wi 4   ↔ wb 209   ∨ wo 861

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210  df-or 862

This theorem is used by:  prmdvdsexp  16853  orbi1rVD  45774  sbc3orgVD  45777