Metamath Proof Explorer


Theorem nfe2

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

Ref Expression
Assertion nfe2 ⊢ Ⅎ x ∃ y ∃ x φ

Proof

Step Hyp Ref Expression
1 excom ⊢ ∃ y ∃ x φ ↔ ∃ x ∃ y φ
2 nfe1 ⊢ Ⅎ x ∃ x ∃ y φ
3 1 2 nfxfr ⊢ Ⅎ x ∃ y ∃ x φ