Theorem pm11.7

Description: Theorem *11.7 in WhiteheadRussell p. 166. (Contributed by Andrew Salmon, 24-May-2011)

	Ref	Expression
Assertion	pm11.7	⊢ ( ∃ 𝑥 ∃ 𝑦 ( 𝜑 ∨ 𝜑 ) ↔ ∃ 𝑥 ∃ 𝑦 𝜑 )

Proof

Step	Hyp	Ref	Expression
1		oridm	⊢ ( ( 𝜑 ∨ 𝜑 ) ↔ 𝜑 )
2	1	2exbii	⊢ ( ∃ 𝑥 ∃ 𝑦 ( 𝜑 ∨ 𝜑 ) ↔ ∃ 𝑥 ∃ 𝑦 𝜑 )