Theorem exdistr2

Description: Distribution of existential quantifiers. (Contributed by NM, 17-Mar-1995)

	Ref	Expression
Assertion	exdistr2	⊢ ( ∃ 𝑥 ∃ 𝑦 ∃ 𝑧 ( 𝜑 ∧ 𝜓 ) ↔ ∃ 𝑥 ( 𝜑 ∧ ∃ 𝑦 ∃ 𝑧 𝜓 ) )

Proof

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