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Theorem orddif 4976
Description: Ordinal derived from its successor. (Contributed by NM, 20-May-1998.)
Assertion
Ref Expression
orddif

Proof of Theorem orddif
StepHypRef Expression
1 orddisj 4921 . 2
2 disj3 3871 . . 3
3 df-suc 4889 . . . . . 6
43difeq1i 3617 . . . . 5
5 difun2 3907 . . . . 5
64, 5eqtri 2486 . . . 4
76eqeq2i 2475 . . 3
82, 7bitr4i 252 . 2
91, 8sylib 196 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  =wceq 1395  \cdif 3472  u.cun 3473  i^icin 3474   c0 3784  {csn 4029  Ordword 4882  succsuc 4885
This theorem is referenced by:  phplem3  7718  phplem4  7719  pssnn  7758
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-9 1822  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435  ax-sep 4573  ax-nul 4581  ax-pr 4691
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-eu 2286  df-mo 2287  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-ral 2812  df-rex 2813  df-rab 2816  df-v 3111  df-sbc 3328  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-if 3942  df-sn 4030  df-pr 4032  df-op 4036  df-br 4453  df-opab 4511  df-eprel 4796  df-fr 4843  df-we 4845  df-ord 4886  df-suc 4889
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