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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 𝑥𝑦𝑥𝜑

Proof of Theorem nfa2
StepHypRef Expression
1 alcom 2186 . 2 (∀𝑦𝑥𝜑 ↔ ∀𝑥𝑦𝜑)
2 nfa1 2177 . 2 𝑥𝑥𝑦𝜑
31, 2nfxfr 1928 1 𝑥𝑦𝑥𝜑
Colors of variables: wff setvar class
Syntax hints:  wal 1630  wnf 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
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