Theorem alcom

Description: Theorem 19.5 of Margaris p. 89. (Contributed by NM, 30-Jun-1993)

	Ref	Expression
Assertion	alcom	⊢ ( ∀ 𝑥 ∀ 𝑦 𝜑 ↔ ∀ 𝑦 ∀ 𝑥 𝜑 )

Proof

Step	Hyp	Ref	Expression
1		ax-11	⊢ ( ∀ 𝑥 ∀ 𝑦 𝜑 → ∀ 𝑦 ∀ 𝑥 𝜑 )
2		ax-11	⊢ ( ∀ 𝑦 ∀ 𝑥 𝜑 → ∀ 𝑥 ∀ 𝑦 𝜑 )
3	1 2	impbii	⊢ ( ∀ 𝑥 ∀ 𝑦 𝜑 ↔ ∀ 𝑦 ∀ 𝑥 𝜑 )