Theorem nfa2 2189

Description: Lemma 24 of [Monk2] p. 114. (Contributed by Mario Carneiro, 24-Sep-2016.) Remove dependency on ax-12 2196. (Revised by Wolf Lammen, 18-Oct-2021.)

Assertion

Ref	Expression
nfa2	⊢ Ⅎ𝑥∀𝑦∀𝑥𝜑

Proof of Theorem nfa2

Step	Hyp	Ref	Expression
1		alcom 2186	. 2 ⊢ (∀𝑦∀𝑥𝜑 ↔ ∀𝑥∀𝑦𝜑)
2		nfa1 2177	. 2 ⊢ Ⅎ𝑥∀𝑥∀𝑦𝜑
3	1, 2	nfxfr 1928	1 ⊢ Ⅎ𝑥∀𝑦∀𝑥𝜑

Syntax hints:  ∀wal 1630  Ⅎwnf 1857

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1871  ax-4 1886  ax-10 2168  ax-11 2183

This theorem depends on definitions:  df-bi 197  df-or 384  df-ex 1854  df-nf 1859

This theorem is referenced by:  cbv1h  2413  csbie2t  3703  copsex2t  5105  fnoprabg  6926  bj-hbext  33007  bj-nfext  33009  bj-cbv1hv  33036  ax11-pm  33125  pm14.123b  39129  hbexg  39274