Theorem nfe2 43017

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 2200	. 2 ⊢ (∃𝑦∃𝑥𝜑 ↔ ∃𝑥∃𝑦𝜑)
2		nfe1 2188	. 2 ⊢ Ⅎ𝑥∃𝑥∃𝑦𝜑
3	1, 2	nfxfr 1886	1 ⊢ Ⅎ𝑥∃𝑦∃𝑥𝜑

This proof depends on syntax axioms:  ∃wex 1812  Ⅎwnf 1816

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842  ax-10 2179  ax-11 2195

This proof depends on definitions:  df-bi 210  df-ex 1813  df-nf 1817

This theorem is used by: (None)