Theorem nfale2 43026

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

Assertion

Ref	Expression
nfale2	⊢ Ⅎ𝑥∀𝑦∃𝑥𝜑

Proof of Theorem nfale2

Step	Hyp	Ref	Expression
1		hbe1 2181	. 2 ⊢ (∃𝑥𝜑 → ∀𝑥∃𝑥𝜑)
2	1	nfalh 43024	1 ⊢ Ⅎ𝑥∀𝑦∃𝑥𝜑

This proof depends on syntax axioms:  ∀wal 1568  ∃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)