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Theorem ordequn 4983
 Description: The maximum (i.e. union) of two ordinals is either one or the other. Similar to Exercise 14 of [TakeutiZaring] p. 40. (Contributed by NM, 28-Nov-2003.)
Assertion
Ref Expression
ordequn

Proof of Theorem ordequn
StepHypRef Expression
1 ordtri2or2 4979 . 2
2 ssequn1 3673 . . . . 5
3 eqeq2 2472 . . . . 5
42, 3sylbi 195 . . . 4
5 olc 384 . . . 4
64, 5syl6bi 228 . . 3
7 ssequn2 3676 . . . . 5
8 eqeq2 2472 . . . . 5
97, 8sylbi 195 . . . 4
10 orc 385 . . . 4
119, 10syl6bi 228 . . 3
126, 11jaoi 379 . 2
131, 12syl 16 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  <->wb 184  \/wo 368  /\wa 369  =wceq 1395  u.cun 3473  C_wss 3475  Ordword 4882 This theorem is referenced by:  ordun  4984  inar1  9174 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-3or 974  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-pss 3491  df-nul 3785  df-if 3942  df-sn 4030  df-pr 4032  df-op 4036  df-uni 4250  df-br 4453  df-opab 4511  df-tr 4546  df-eprel 4796  df-po 4805  df-so 4806  df-fr 4843  df-we 4845  df-ord 4886
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