Theorem nfe2 42319

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 2167	. 2 ⊢ (∃𝑦∃𝑥𝜑 ↔ ∃𝑥∃𝑦𝜑)
2		nfe1 2155	. 2 ⊢ Ⅎ𝑥∃𝑥∃𝑦𝜑
3	1, 2	nfxfr 1854	1 ⊢ Ⅎ𝑥∃𝑦∃𝑥𝜑

Syntax hints:  ∃wex 1780  Ⅎwnf 1784

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-10 2146  ax-11 2162

This theorem depends on definitions:  df-bi 207  df-ex 1781  df-nf 1785

This theorem is referenced by: (None)