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Theorem tron 4119
 Description: The class of all ordinal numbers is transitive. (Contributed by NM, 4-May-2009.)
Assertion
Ref Expression
tron

Proof of Theorem tron
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 dftr3 3858 . 2
2 vex 2560 . . . . . . 7
32elon 4111 . . . . . 6
4 ordelord 4118 . . . . . 6
53, 4sylanb 268 . . . . 5
65ex 108 . . . 4
7 vex 2560 . . . . 5
87elon 4111 . . . 4
96, 8syl6ibr 151 . . 3
109ssrdv 2951 . 2
111, 10mprgbir 2379 1
 Colors of variables: wff set class Syntax hints:   wcel 1393   wss 2917   wtr 3854   word 4099  con0 4100 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-3an 887  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-v 2559  df-in 2924  df-ss 2931  df-uni 3581  df-tr 3855  df-iord 4103  df-on 4105 This theorem is referenced by:  ordon  4212  tfi  4305
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