Theorem nfexa2 2211

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 2180	. 2 ⊢ (∃𝑥∀𝑥𝜑 → ∀𝑥𝜑)
2	1	nfexhe 2210	1 ⊢ Ⅎ𝑥∃𝑦∀𝑥𝜑

This proof depends on syntax axioms:  ∀wal 1567  ∃wex 1811  Ⅎwnf 1815

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1827  ax-4 1841  ax-10 2177  ax-11 2193

This proof depends on definitions:  df-bi 210  df-ex 1812  df-nf 1816

This theorem is used by:  nfmo1  2582  nfeu1ALT  2613