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Metamath Proof Explorer

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 )