Theorem nfe2 42700

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

Assertion

Ref	Expression
nfe2	⊢ Ⅎ𝑥∃𝑦∃𝑥𝜑

Proof of Theorem nfe2

Step	Hyp	Ref	Expression
1		excom 2173	. 2 ⊢ (∃𝑦∃𝑥𝜑 ↔ ∃𝑥∃𝑦𝜑)
2		nfe1 2161	. 2 ⊢ Ⅎ𝑥∃𝑥∃𝑦𝜑
3	1, 2	nfxfr 1860	1 ⊢ Ⅎ𝑥∃𝑦∃𝑥𝜑

Syntax hints:  ∃wex 1786  Ⅎwnf 1790

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1802  ax-4 1816  ax-10 2152  ax-11 2168

This theorem depends on definitions:  df-bi 208  df-ex 1787  df-nf 1791

This theorem is referenced by: (None)