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Theorem axacndlem3 9031
 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 2149 . . . 4
2 simpl 459 . . . . . 6
32alimi 1683 . . . . 5
4 nd3 9011 . . . . . 6
54pm2.21d 110 . . . . 5
63, 5syl5 33 . . . 4
71, 6alrimi 1954 . . 3
87axc4i 1979 . 2
9 19.8a 1934 . 2
108, 9syl 17 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 188   wa 371  wal 1441  wex 1662 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1668  ax-4 1681  ax-5 1757  ax-6 1804  ax-7 1850  ax-9 1895  ax-10 1914  ax-11 1919  ax-12 1932  ax-13 2090  ax-ext 2430  ax-sep 4524  ax-nul 4533  ax-pr 4638  ax-reg 8104 This theorem depends on definitions:  df-bi 189  df-or 372  df-an 373  df-tru 1446  df-ex 1663  df-nf 1667  df-sb 1797  df-clab 2437  df-cleq 2443  df-clel 2446  df-nfc 2580  df-ne 2623  df-ral 2741  df-rex 2742  df-v 3046  df-dif 3406  df-un 3408  df-nul 3731  df-sn 3968  df-pr 3970 This theorem is referenced by:  axacndlem5  9033  axacnd  9034
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