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Theorem ontr1 4375
 Description: Transitive law for ordinal numbers. Theorem 7M(b) of [Enderton] p. 192. (Contributed by NM, 11-Aug-1994.)
Assertion
Ref Expression
ontr1

Proof of Theorem ontr1
StepHypRef Expression
1 eloni 4339 . 2
2 ordtr1 4372 . 2
31, 2syl 17 1
 Colors of variables: wff set class Syntax hints:   wi 6   wa 360   wcel 1621   word 4328  con0 4329 This theorem is referenced by:  smoiun  6311  dif20el  6437  oeordi  6518  omabs  6578  omsmolem  6584  cofsmo  7828  cfsmolem  7829  inar1  8330  grur1a  8374 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-17 1628  ax-12o 1664  ax-10 1678  ax-9 1684  ax-4 1692  ax-16 1927  ax-ext 2237 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1315  df-ex 1538  df-nf 1540  df-sb 1884  df-clab 2243  df-cleq 2249  df-clel 2252  df-nfc 2381  df-ral 2520  df-rex 2521  df-v 2742  df-in 3101  df-ss 3108  df-uni 3769  df-tr 4054  df-po 4251  df-so 4252  df-fr 4289  df-we 4291  df-ord 4332  df-on 4333
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