Theorem nfa2 2182

Description: Lemma 24 of [Monk2] p. 114. (Contributed by Mario Carneiro, 24-Sep-2016.) Remove dependency on ax-12 2185. (Revised by Wolf Lammen, 18-Oct-2021.)

Assertion

Ref	Expression
nfa2	⊢ Ⅎ𝑥∀𝑦∀𝑥𝜑

Proof of Theorem nfa2

Step	Hyp	Ref	Expression
1		alcom 2165	. 2 ⊢ (∀𝑦∀𝑥𝜑 ↔ ∀𝑥∀𝑦𝜑)
2		nfa1 2157	. 2 ⊢ Ⅎ𝑥∀𝑥∀𝑦𝜑
3	1, 2	nfxfr 1855	1 ⊢ Ⅎ𝑥∀𝑦∀𝑥𝜑

Syntax hints:  ∀wal 1540  Ⅎwnf 1785

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-10 2147  ax-11 2163

This theorem depends on definitions:  df-bi 207  df-or 849  df-ex 1782  df-nf 1786

This theorem is referenced by:  cbv1h  2410  nfra2w  3274  csbie2t  3889  copsex2t  5448  fnoprabg  7491  bj-hbext  36949  bj-nfext  36951  bj-cbv1hv  37038  ax11-pm  37074  pm14.123b  44776  hbexg  44906  nfich2  47802  ich2al  47821