Theorem 3exbidv

Description: Formula-building rule for three existential quantifiers (deduction form). (Contributed by NM, 1-May-1995)

	Ref	Expression
Hypothesis	3exbidv.1	⊢ ( 𝜑 → ( 𝜓 ↔ 𝜒 ) )
Assertion	3exbidv	⊢ ( 𝜑 → ( ∃ 𝑥 ∃ 𝑦 ∃ 𝑧 𝜓 ↔ ∃ 𝑥 ∃ 𝑦 ∃ 𝑧 𝜒 ) )

Proof

Step	Hyp	Ref	Expression
1		3exbidv.1	⊢ ( 𝜑 → ( 𝜓 ↔ 𝜒 ) )
2	1	exbidv	⊢ ( 𝜑 → ( ∃ 𝑧 𝜓 ↔ ∃ 𝑧 𝜒 ) )
3	2	2exbidv	⊢ ( 𝜑 → ( ∃ 𝑥 ∃ 𝑦 ∃ 𝑧 𝜓 ↔ ∃ 𝑥 ∃ 𝑦 ∃ 𝑧 𝜒 ) )