Theorem nfa2 2212

Description: Lemma 24 of [Monk2] p. 114. (Contributed by Mario Carneiro, 24-Sep-2016.) Remove dependency on ax-12 2215. (Revised by Wolf Lammen, 18-Oct-2021.)

Assertion

Ref	Expression
nfa2	⊢ Ⅎ𝑥∀𝑦∀𝑥𝜑

Proof of Theorem nfa2

Step	Hyp	Ref	Expression
1		alcom 2196	. 2 ⊢ (∀𝑦∀𝑥𝜑 ↔ ∀𝑥∀𝑦𝜑)
2		nfa1 2188	. 2 ⊢ Ⅎ𝑥∀𝑥∀𝑦𝜑
3	1, 2	nfxfr 1876	1 ⊢ Ⅎ𝑥∀𝑦∀𝑥𝜑

Syntax hints:  ∀wal 1561  Ⅎwnf 1806

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1818  ax-4 1832  ax-10 2178  ax-11 2194

This theorem depends on definitions:  df-bi 210  df-or 861  df-ex 1803  df-nf 1807

This theorem is referenced by:  cbv1h  2439  nfra2w  3301  csbie2t  3893  copsex2t  5466  fnoprabg  7523  bj-nfext  37201  bj-cbv1hv  37293  ax11-pm  37329  pm14.123b  45000  hbexg  45130  nfich2  48052  ich2al  48071