Theorem pm10.12

Description: Theorem *10.12 in WhiteheadRussell p. 146. In *10, this is treated as an axiom, and the proofs in *10 are based on this theorem. (Contributed by Andrew Salmon, 17-Jun-2011)

	Ref	Expression
Assertion	pm10.12	⊢ ( ∀ 𝑥 ( 𝜑 ∨ 𝜓 ) → ( 𝜑 ∨ ∀ 𝑥 𝜓 ) )

Proof

Step	Hyp	Ref	Expression
1		19.32v	⊢ ( ∀ 𝑥 ( 𝜑 ∨ 𝜓 ) ↔ ( 𝜑 ∨ ∀ 𝑥 𝜓 ) )
2	1	biimpi	⊢ ( ∀ 𝑥 ( 𝜑 ∨ 𝜓 ) → ( 𝜑 ∨ ∀ 𝑥 𝜓 ) )