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Theorem nordeq 4268
 Description: A member of an ordinal class is not equal to it. (Contributed by NM, 25-May-1998.)
Assertion
Ref Expression
nordeq

Proof of Theorem nordeq
StepHypRef Expression
1 ordirr 4267 . . . 4
2 eleq1 2100 . . . . 5
32notbid 592 . . . 4
41, 3syl5ibcom 144 . . 3
54necon2ad 2262 . 2
65imp 115 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wa 97   wceq 1243   wcel 1393   wne 2204   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-in1 544  ax-in2 545  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  ax-setind 4262 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-ne 2206  df-ral 2311  df-v 2559  df-dif 2920  df-sn 3381 This theorem is referenced by:  phplem1  6315
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