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Theorem ordelord 4118
 Description: An element of an ordinal class is ordinal. Proposition 7.6 of [TakeutiZaring] p. 36. (Contributed by NM, 23-Apr-1994.)
Assertion
Ref Expression
ordelord

Proof of Theorem ordelord
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 eleq1 2100 . . . . 5
21anbi2d 437 . . . 4
3 ordeq 4109 . . . 4
42, 3imbi12d 223 . . 3
5 dford3 4104 . . . . . 6
65simprbi 260 . . . . 5
76r19.21bi 2407 . . . 4
8 ordelss 4116 . . . 4
9 simpl 102 . . . 4
10 trssord 4117 . . . 4
117, 8, 9, 10syl3anc 1135 . . 3
124, 11vtoclg 2613 . 2
1312anabsi7 515 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 97   wceq 1243   wcel 1393  wral 2306   wss 2917   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-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 This theorem is referenced by:  tron  4119  ordelon  4120  ordsucg  4228  ordwe  4300  smores  5907
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