Theorem nfale2 42320

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 2148	. 2 ⊢ (∃𝑥𝜑 → ∀𝑥∃𝑥𝜑)
2	1	nfalh 42318	1 ⊢ Ⅎ𝑥∀𝑦∃𝑥𝜑

Syntax hints:  ∀wal 1539  ∃wex 1780  Ⅎwnf 1784

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-10 2146  ax-11 2162

This theorem depends on definitions:  df-bi 207  df-ex 1781  df-nf 1785

This theorem is referenced by: (None)