Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  axacndlem3 Structured version   Unicode version

Theorem axacndlem3 8485
 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 2043 . . . 4
2 simpl 445 . . . . . 6
32alimi 1569 . . . . 5
4 nd3 8465 . . . . . 6
54pm2.21d 101 . . . . 5
63, 5syl5 31 . . . 4
71, 6alrimi 1782 . . 3
87a5i 1808 . 2
9 19.8a 1763 . 2
108, 9syl 16 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 178   wa 360  wal 1550  wex 1551 This theorem is referenced by:  axacndlem5  8487  axacnd  8488 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-14 1730  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2418  ax-sep 4331  ax-nul 4339  ax-pr 4404  ax-reg 7561 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2424  df-cleq 2430  df-clel 2433  df-nfc 2562  df-ne 2602  df-ral 2711  df-rex 2712  df-v 2959  df-dif 3324  df-un 3326  df-nul 3630  df-sn 3821  df-pr 3822
 Copyright terms: Public domain W3C validator