Theorem alcoms 2199

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

Hypothesis

Ref	Expression
alcoms.1	⊢ (∀𝑥∀𝑦𝜑 → 𝜓)

Assertion

Ref	Expression
alcoms	⊢ (∀𝑦∀𝑥𝜑 → 𝜓)

Proof of Theorem alcoms

Step	Hyp	Ref	Expression
1		ax-11 2198	. 2 ⊢ (∀𝑦∀𝑥𝜑 → ∀𝑥∀𝑦𝜑)
2		alcoms.1	. 2 ⊢ (∀𝑥∀𝑦𝜑 → 𝜓)
3	1, 2	syl 18	1 ⊢ (∀𝑦∀𝑥𝜑 → 𝜓)

Syntax hints:   → wi 4  ∀wal 1565

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-11 2198

This theorem is referenced by:  cbv2h  2444  mo3  2598  bj-nfalt  37223  bj-cbv3ta  37306  bj-cbv2hv  37317  wl-equsal1i  38082  wl-mo3t  38114  axc11n-16  39597  axc11next  45001