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Theorem orddif 4678
 Description: Ordinal derived from its successor. (Contributed by NM, 20-May-1998.)
Assertion
Ref Expression
orddif

Proof of Theorem orddif
StepHypRef Expression
1 orddisj 4622 . 2
2 disj3 3674 . . 3
3 df-suc 4590 . . . . . 6
43difeq1i 3463 . . . . 5
5 difun2 3709 . . . . 5
64, 5eqtri 2458 . . . 4
76eqeq2i 2448 . . 3
82, 7bitr4i 245 . 2
91, 8sylib 190 1
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1653   cdif 3319   cun 3320   cin 3321  c0 3630  csn 3816   word 4583   csuc 4586 This theorem is referenced by:  phplem3  7291  phplem4  7292  pssnn  7330 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-14 1730  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419  ax-sep 4333  ax-nul 4341  ax-pr 4406 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-eu 2287  df-mo 2288  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ne 2603  df-ral 2712  df-rex 2713  df-rab 2716  df-v 2960  df-sbc 3164  df-dif 3325  df-un 3327  df-in 3329  df-ss 3336  df-nul 3631  df-if 3742  df-sn 3822  df-pr 3823  df-op 3825  df-br 4216  df-opab 4270  df-eprel 4497  df-fr 4544  df-we 4546  df-ord 4587  df-suc 4590
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