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Theorem nd1 8500
 Description: A lemma for proving conditionless ZFC axioms. (Contributed by NM, 1-Jan-2002.)
Assertion
Ref Expression
nd1

Proof of Theorem nd1
StepHypRef Expression
1 elirrv 7601 . . 3
2 stdpc4 2095 . . . 4
31nfnth 1566 . . . . 5
4 elequ1 1731 . . . . 5
53, 4sbie 2155 . . . 4
62, 5sylib 190 . . 3
71, 6mto 170 . 2
8 ax10o 2042 . 2
97, 8mtoi 172 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4  wal 1550  wsb 1660 This theorem is referenced by:  axrepnd  8507  axinfndlem1  8518  axinfnd  8519  axacndlem1  8520  axacndlem2  8521 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1628  ax-9 1669  ax-8 1690  ax-13 1730  ax-14 1732  ax-6 1747  ax-7 1752  ax-11 1764  ax-12 1954  ax-ext 2424  ax-sep 4361  ax-nul 4369  ax-pr 4438  ax-reg 7596 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 1661  df-clab 2430  df-cleq 2436  df-clel 2439  df-nfc 2568  df-ne 2608  df-ral 2717  df-rex 2718  df-v 2967  df-dif 3312  df-un 3314  df-nul 3617  df-sn 3849  df-pr 3850
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