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Theorem tz7.5 4904
Description: A subclass (possibly proper) of an ordinal class has a minimal element. Proposition 7.5 of [TakeutiZaring] p. 36. (Contributed by NM, 18-Feb-2004.) (Revised by David Abernethy, 16-Mar-2011.)
Assertion
Ref Expression
tz7.5
Distinct variable group:   ,

Proof of Theorem tz7.5
StepHypRef Expression
1 ordwe 4896 . 2
2 wefrc 4878 . 2
31, 2syl3an1 1261 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  /\w3a 973  =wceq 1395  =/=wne 2652  E.wrex 2808  i^icin 3474  C_wss 3475   c0 3784   cep 4794  Wewwe 4842  Ordword 4882
This theorem is referenced by:  tz7.7  4909  onint  6630  tfi  6688  peano5  6723  fin23lem26  8726
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
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-eu 2286  df-mo 2287  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-ral 2812  df-rex 2813  df-rab 2816  df-v 3111  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-if 3942  df-sn 4030  df-pr 4032  df-op 4036  df-br 4453  df-opab 4511  df-eprel 4796  df-po 4805  df-so 4806  df-fr 4843  df-we 4845  df-ord 4886
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