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Theorem axacndlem3 9008
 Description: Lemma for the Axiom of Choice with no distinct variable conditions. (Contributed by NM, 3-Jan-2002.)
Assertion
Ref Expression
axacndlem3

Proof of Theorem axacndlem3
StepHypRef Expression
1 nfae 2056 . . . 4
2 simpl 457 . . . . . 6
32alimi 1633 . . . . 5
4 nd3 8985 . . . . . 6
54pm2.21d 106 . . . . 5
63, 5syl5 32 . . . 4
71, 6alrimi 1877 . . 3
87axc4i 1898 . 2
9 19.8a 1857 . 2
108, 9syl 16 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  <->wb 184  /\wa 369  A.wal 1393  E.wex 1612 This theorem is referenced by:  axacndlem5  9010  axacnd  9011 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-9 1822  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435  ax-sep 4573  ax-nul 4581  ax-pr 4691  ax-reg 8039 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-ral 2812  df-rex 2813  df-v 3111  df-dif 3478  df-un 3480  df-nul 3785  df-sn 4030  df-pr 4032
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