Theorem nfale2 42966

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 2178	. 2 ⊢ (∃𝑥𝜑 → ∀𝑥∃𝑥𝜑)
2	1	nfalh 42964	1 ⊢ Ⅎ𝑥∀𝑦∃𝑥𝜑

Syntax hints:  ∀wal 1568  ∃wex 1809  Ⅎwnf 1813

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1825  ax-4 1839  ax-10 2176  ax-11 2192

This theorem depends on definitions:  df-bi 210  df-ex 1810  df-nf 1814

This theorem is referenced by: (None)