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Theorem nfa2 2166
Description: Lemma 24 of [Monk2] p. 114. (Contributed by Mario Carneiro, 24-Sep-2016.) Remove dependency on ax-12 2167. (Revised by Wolf Lammen, 18-Oct-2021.)
Assertion
Ref Expression
nfa2 𝑥𝑦𝑥𝜑

Proof of Theorem nfa2
StepHypRef Expression
1 alcom 2154 . 2 (∀𝑦𝑥𝜑 ↔ ∀𝑥𝑦𝜑)
2 nfa1 2147 . 2 𝑥𝑥𝑦𝜑
31, 2nfxfr 1846 1 𝑥𝑦𝑥𝜑
Colors of variables: wff setvar class
Syntax hints:  wal 1528  wnf 1777
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-10 2137  ax-11 2152
This theorem depends on definitions:  df-bi 208  df-or 844  df-ex 1774  df-nf 1778
This theorem is referenced by:  cbv1h  2421  csbie2t  3924  copsex2t  5379  fnoprabg  7268  bj-hbext  33929  bj-nfext  33931  bj-cbv1hv  34003  ax11-pm  34040  pm14.123b  40620  hbexg  40752  nfich2  43437  dfich2bi  43444  ich2al  43457
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