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Theorem tz7.5 4306
 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:   ,
Allowed substitution hint:   ()

Proof of Theorem tz7.5
StepHypRef Expression
1 ordwe 4298 . 2
2 wefrc 4280 . 2
31, 2syl3an1 1220 1
 Colors of variables: wff set class Syntax hints:   wi 6   w3a 939   wceq 1619   wne 2412  wrex 2510   cin 3077   wss 3078  c0 3362   cep 4196   wwe 4244   word 4284 This theorem is referenced by:  tz7.7  4311  onint  4477  tfi  4535  peano5  4570  fin23lem26  7835 This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-7 1535  ax-gen 1536  ax-8 1623  ax-11 1624  ax-14 1626  ax-17 1628  ax-12o 1664  ax-10 1678  ax-9 1684  ax-4 1692  ax-16 1926  ax-ext 2234  ax-sep 4038  ax-nul 4046  ax-pr 4108 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 941  df-tru 1315  df-ex 1538  df-nf 1540  df-sb 1883  df-eu 2118  df-mo 2119  df-clab 2240  df-cleq 2246  df-clel 2249  df-nfc 2374  df-ne 2414  df-ral 2513  df-rex 2514  df-rab 2516  df-v 2729  df-dif 3081  df-un 3083  df-in 3085  df-ss 3089  df-nul 3363  df-if 3471  df-sn 3550  df-pr 3551  df-op 3553  df-br 3921  df-opab 3975  df-eprel 4198  df-po 4207  df-so 4208  df-fr 4245  df-we 4247  df-ord 4288
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