Theorem exdistr

Description: Distribution of existential quantifiers. See also exdistrv . (Contributed by NM, 9-Mar-1995)

	Ref	Expression
Assertion	exdistr	⊢ ( ∃ 𝑥 ∃ 𝑦 ( 𝜑 ∧ 𝜓 ) ↔ ∃ 𝑥 ( 𝜑 ∧ ∃ 𝑦 𝜓 ) )

Proof

Step	Hyp	Ref	Expression
1		19.42v	⊢ ( ∃ 𝑦 ( 𝜑 ∧ 𝜓 ) ↔ ( 𝜑 ∧ ∃ 𝑦 𝜓 ) )
2	1	exbii	⊢ ( ∃ 𝑥 ∃ 𝑦 ( 𝜑 ∧ 𝜓 ) ↔ ∃ 𝑥 ( 𝜑 ∧ ∃ 𝑦 𝜓 ) )