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Theorem nd2 8453
 Description: A lemma for proving conditionless ZFC axioms. (Contributed by NM, 1-Jan-2002.)
Assertion
Ref Expression
nd2

Proof of Theorem nd2
StepHypRef Expression
1 elirrv 7555 . . 3
2 stdpc4 2087 . . . 4
31nfnth 1565 . . . . 5
4 elequ2 1730 . . . . 5
53, 4sbie 2122 . . . 4
62, 5sylib 189 . . 3
71, 6mto 169 . 2
8 ax10o 2038 . 2
97, 8mtoi 171 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4  wal 1549  wsb 1658 This theorem is referenced by:  axrepnd  8459  axpownd  8466  axinfndlem1  8470  axacndlem4  8475 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416  ax-sep 4322  ax-nul 4330  ax-pr 4395  ax-reg 7550 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ne 2600  df-ral 2702  df-rex 2703  df-v 2950  df-dif 3315  df-un 3317  df-nul 3621  df-sn 3812  df-pr 3813
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