Theorem pm10.42

Description: Theorem *10.42 in WhiteheadRussell p. 155. (Contributed by Andrew Salmon, 17-Jun-2011)

	Ref	Expression
Assertion	pm10.42	⊢ ( ( ∃ 𝑥 𝜑 ∨ ∃ 𝑥 𝜓 ) ↔ ∃ 𝑥 ( 𝜑 ∨ 𝜓 ) )

Proof

Step	Hyp	Ref	Expression
1		19.43	⊢ ( ∃ 𝑥 ( 𝜑 ∨ 𝜓 ) ↔ ( ∃ 𝑥 𝜑 ∨ ∃ 𝑥 𝜓 ) )
2	1	bicomi	⊢ ( ( ∃ 𝑥 𝜑 ∨ ∃ 𝑥 𝜓 ) ↔ ∃ 𝑥 ( 𝜑 ∨ 𝜓 ) )