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Theorem ordequn 4668
 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 4664 . 2
2 ssequn1 3504 . . . . 5
3 eqeq2 2439 . . . . 5
42, 3sylbi 188 . . . 4
5 olc 374 . . . 4
64, 5syl6bi 220 . . 3
7 ssequn2 3507 . . . . 5
8 eqeq2 2439 . . . . 5
97, 8sylbi 188 . . . 4
10 orc 375 . . . 4
119, 10syl6bi 220 . . 3
126, 11jaoi 369 . 2
131, 12syl 16 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wo 358   wa 359   wceq 1652   cun 3305   wss 3307   word 4567 This theorem is referenced by:  ordun  4669  inar1  8634 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2411  ax-sep 4317  ax-nul 4325  ax-pr 4390 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3or 937  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-eu 2284  df-mo 2285  df-clab 2417  df-cleq 2423  df-clel 2426  df-nfc 2555  df-ne 2595  df-ral 2697  df-rex 2698  df-rab 2701  df-v 2945  df-sbc 3149  df-dif 3310  df-un 3312  df-in 3314  df-ss 3321  df-pss 3323  df-nul 3616  df-if 3727  df-sn 3807  df-pr 3808  df-op 3810  df-uni 4003  df-br 4200  df-opab 4254  df-tr 4290  df-eprel 4481  df-po 4490  df-so 4491  df-fr 4528  df-we 4530  df-ord 4571
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