Theorem orbi1 686

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 19	. 2 ⊢ ((φ ↔ ψ) → (φ ↔ ψ))
2	1	orbi1d 683	1 ⊢ ((φ ↔ ψ) → ((φ ∨ χ) ↔ (ψ ∨ χ)))

This proof depends on syntax axioms:   → wi 4   ↔ wb 176   ∨ wo 357

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

This proof depends on definitions:  df-bi 177  df-or 359

This theorem is used by: (None)