Theorem alcoms

Description: Swap quantifiers in an antecedent. (Contributed by NM, 11-May-1993)

	Ref	Expression
Hypothesis	alcoms.1	⊢ ( ∀ 𝑥 ∀ 𝑦 𝜑 → 𝜓 )
Assertion	alcoms	⊢ ( ∀ 𝑦 ∀ 𝑥 𝜑 → 𝜓 )

Proof

Step	Hyp	Ref	Expression
1		alcoms.1	⊢ ( ∀ 𝑥 ∀ 𝑦 𝜑 → 𝜓 )
2		ax-11	⊢ ( ∀ 𝑦 ∀ 𝑥 𝜑 → ∀ 𝑥 ∀ 𝑦 𝜑 )
3	2 1	syl	⊢ ( ∀ 𝑦 ∀ 𝑥 𝜑 → 𝜓 )