Theorem nfexa2 2214

Description: An inner universal quantifier's variable is bound. (Contributed by SN, 11-Feb-2026.)

Assertion

Ref	Expression
nfexa2	⊢ Ⅎ𝑥∃𝑦∀𝑥𝜑

Proof of Theorem nfexa2

Step	Hyp	Ref	Expression
1		hbe1a 2181	. 2 ⊢ (∃𝑥∀𝑥𝜑 → ∀𝑥𝜑)
2	1	nfexhe 2213	1 ⊢ Ⅎ𝑥∃𝑦∀𝑥𝜑

Syntax hints:  ∀wal 1561  ∃wex 1802  Ⅎwnf 1806

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1818  ax-4 1832  ax-10 2178  ax-11 2194

This theorem depends on definitions:  df-bi 210  df-ex 1803  df-nf 1807

This theorem is referenced by:  nfmo1  2587  nfeu1ALT  2618