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Theorem ordeq 4109
 Description: Equality theorem for the ordinal predicate. (Contributed by NM, 17-Sep-1993.)
Assertion
Ref Expression
ordeq

Proof of Theorem ordeq
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 treq 3860 . . 3
2 raleq 2505 . . 3
31, 2anbi12d 442 . 2
4 dford3 4104 . 2
5 dford3 4104 . 2
63, 4, 53bitr4g 212 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 97   wb 98   wceq 1243  wral 2306   wtr 3854   word 4099 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-ral 2311  df-rex 2312  df-in 2924  df-ss 2931  df-uni 3581  df-tr 3855  df-iord 4103 This theorem is referenced by:  elong  4110  limeq  4114  ordelord  4118  ordtriexmidlem  4245  2ordpr  4249  issmo  5903  issmo2  5904  smoeq  5905  smores  5907  smores2  5909  smodm2  5910  smoiso  5917  tfrlem8  5934
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