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Theorem nfa2 2170
Description: Lemma 24 of [Monk2] p. 114. (Contributed by Mario Carneiro, 24-Sep-2016.) Remove dependency on ax-12 2171. (Revised by Wolf Lammen, 18-Oct-2021.)
Assertion
Ref Expression
nfa2 𝑥𝑦𝑥𝜑

Proof of Theorem nfa2
StepHypRef Expression
1 alcom 2156 . 2 (∀𝑦𝑥𝜑 ↔ ∀𝑥𝑦𝜑)
2 nfa1 2148 . 2 𝑥𝑥𝑦𝜑
31, 2nfxfr 1855 1 𝑥𝑦𝑥𝜑
Colors of variables: wff setvar class
Syntax hints:  wal 1537  wnf 1786
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-10 2137  ax-11 2154
This theorem depends on definitions:  df-bi 206  df-or 845  df-ex 1783  df-nf 1787
This theorem is referenced by:  cbv1h  2405  csbie2t  3872  copsex2t  5404  fnoprabg  7387  bj-hbext  34900  bj-nfext  34902  bj-cbv1hv  34986  ax11-pm  35023  pm14.123b  42025  hbexg  42157  nfich2  44878  ich2al  44897
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