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Theorem nfa2 2176
Description: Lemma 24 of [Monk2] p. 114. (Contributed by Mario Carneiro, 24-Sep-2016.) Remove dependency on ax-12 2177. (Revised by Wolf Lammen, 18-Oct-2021.)
Assertion
Ref Expression
nfa2 𝑥𝑦𝑥𝜑

Proof of Theorem nfa2
StepHypRef Expression
1 alcom 2159 . 2 (∀𝑦𝑥𝜑 ↔ ∀𝑥𝑦𝜑)
2 nfa1 2151 . 2 𝑥𝑥𝑦𝜑
31, 2nfxfr 1853 1 𝑥𝑦𝑥𝜑
Colors of variables: wff setvar class
Syntax hints:  wal 1538  wnf 1783
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-10 2141  ax-11 2157
This theorem depends on definitions:  df-bi 207  df-or 849  df-ex 1780  df-nf 1784
This theorem is referenced by:  cbv1h  2410  nfra2w  3299  csbie2t  3937  copsex2t  5497  fnoprabg  7556  bj-hbext  36711  bj-nfext  36713  bj-cbv1hv  36797  ax11-pm  36833  pm14.123b  44445  hbexg  44576  nfich2  47435  ich2al  47454
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