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Theorem ss1oel2o 13536
 Description: Any subset of ordinal one being an element of ordinal two is equivalent to excluded middle. A variation of exmid01 4159 which more directly illustrates the contrast with el2oss1o 6387. (Contributed by Jim Kingdon, 8-Aug-2022.)
Assertion
Ref Expression
ss1oel2o EXMID

Proof of Theorem ss1oel2o
StepHypRef Expression
1 exmid01 4159 . 2 EXMID
2 df1o2 6373 . . . . 5
32sseq2i 3155 . . . 4
4 df2o2 6375 . . . . . 6
54eleq2i 2224 . . . . 5
6 vex 2715 . . . . . 6
76elpr 3581 . . . . 5
85, 7bitri 183 . . . 4
93, 8imbi12i 238 . . 3
109albii 1450 . 2
111, 10bitr4i 186 1 EXMID
 Colors of variables: wff set class Syntax hints:   wi 4   wb 104   wo 698  wal 1333   wceq 1335   wcel 2128   wss 3102  c0 3394  csn 3560  cpr 3561  EXMIDwem 4155  c1o 6353  c2o 6354 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 604  ax-in2 605  ax-io 699  ax-5 1427  ax-7 1428  ax-gen 1429  ax-ie1 1473  ax-ie2 1474  ax-8 1484  ax-10 1485  ax-11 1486  ax-i12 1487  ax-bndl 1489  ax-4 1490  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2139  ax-nul 4090 This theorem depends on definitions:  df-bi 116  df-dc 821  df-tru 1338  df-nf 1441  df-sb 1743  df-clab 2144  df-cleq 2150  df-clel 2153  df-nfc 2288  df-v 2714  df-dif 3104  df-un 3106  df-in 3108  df-ss 3115  df-nul 3395  df-sn 3566  df-pr 3567  df-exmid 4156  df-suc 4331  df-1o 6360  df-2o 6361 This theorem is referenced by: (None)
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