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Theorem nfa2 2026
Description: Lemma 24 of [Monk2] p. 114. (Contributed by Mario Carneiro, 24-Sep-2016.) Remove dependency on ax-12 2033. (Revised by Wolf Lammen, 18-Oct-2021.)
Assertion
Ref Expression
nfa2 𝑥𝑦𝑥𝜑

Proof of Theorem nfa2
StepHypRef Expression
1 alcom 2023 . 2 (∀𝑦𝑥𝜑 ↔ ∀𝑥𝑦𝜑)
2 nfa1 2014 . 2 𝑥𝑥𝑦𝜑
31, 2nfxfr 1770 1 𝑥𝑦𝑥𝜑
Colors of variables: wff setvar class
Syntax hints:  wal 1472  wnf 1698
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1712  ax-4 1727  ax-10 2005  ax-11 2020
This theorem depends on definitions:  df-bi 195  df-or 383  df-ex 1695  df-nf 1700
This theorem is referenced by:  cbv1h  2255  csbie2t  3527  copsex2t  4877  fnoprabg  6637  bj-hbext  31722  bj-nfext  31724  bj-cbv1hv  31751  ax11-pm  31841  pm14.123b  37473  hbexg  37617
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