Metamath Proof Explorer


Theorem nfale2

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

Ref Expression
Assertion nfale2 Ⅎ 𝑥 ∀ 𝑦 ∃ 𝑥 𝜑

Proof

Step Hyp Ref Expression
1 hbe1 ⊢ ( ∃ 𝑥 𝜑 → ∀ 𝑥 ∃ 𝑥 𝜑 )
2 1 nfalh ⊢ Ⅎ 𝑥 ∀ 𝑦 ∃ 𝑥 𝜑