Theorem exrot3

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

	Ref	Expression
Assertion	exrot3	⊢ ( ∃ 𝑥 ∃ 𝑦 ∃ 𝑧 𝜑 ↔ ∃ 𝑦 ∃ 𝑧 ∃ 𝑥 𝜑 )

Proof

Step	Hyp	Ref	Expression
1		excom13	⊢ ( ∃ 𝑥 ∃ 𝑦 ∃ 𝑧 𝜑 ↔ ∃ 𝑧 ∃ 𝑦 ∃ 𝑥 𝜑 )
2		excom	⊢ ( ∃ 𝑧 ∃ 𝑦 ∃ 𝑥 𝜑 ↔ ∃ 𝑦 ∃ 𝑧 ∃ 𝑥 𝜑 )
3	1 2	bitri	⊢ ( ∃ 𝑥 ∃ 𝑦 ∃ 𝑧 𝜑 ↔ ∃ 𝑦 ∃ 𝑧 ∃ 𝑥 𝜑 )