Theorem 19.42vvvOLD

Description: Obsolete version of 19.42vvv as of 27-Aug-2023. (Contributed by NM, 21-Sep-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Assertion	19.42vvvOLD	⊢ ( ∃ 𝑥 ∃ 𝑦 ∃ 𝑧 ( 𝜑 ∧ 𝜓 ) ↔ ( 𝜑 ∧ ∃ 𝑥 ∃ 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 ) )
3		19.42v	⊢ ( ∃ 𝑥 ( 𝜑 ∧ ∃ 𝑦 ∃ 𝑧 𝜓 ) ↔ ( 𝜑 ∧ ∃ 𝑥 ∃ 𝑦 ∃ 𝑧 𝜓 ) )
4	2 3	bitri	⊢ ( ∃ 𝑥 ∃ 𝑦 ∃ 𝑧 ( 𝜑 ∧ 𝜓 ) ↔ ( 𝜑 ∧ ∃ 𝑥 ∃ 𝑦 ∃ 𝑧 𝜓 ) )