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Theorem el1o 5935
Description: Membership in ordinal one. (Contributed by NM, 5-Jan-2005.)
Assertion
Ref Expression
el1o (A 1𝑜A = ∅)

Proof of Theorem el1o
StepHypRef Expression
1 df1o2 5928 . . 3 1𝑜 = {∅}
21eleq2i 2086 . 2 (A 1𝑜A {∅})
3 0ex 3858 . . 3 V
43elsnc2 3380 . 2 (A {∅} ↔ A = ∅)
52, 4bitri 173 1 (A 1𝑜A = ∅)
Colors of variables: wff set class
Syntax hints:  wb 98   = wceq 1228   wcel 1374  c0 3201  {csn 3350  1𝑜c1o 5909
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 532  ax-in2 533  ax-io 617  ax-5 1316  ax-7 1317  ax-gen 1318  ax-ie1 1363  ax-ie2 1364  ax-8 1376  ax-10 1377  ax-11 1378  ax-i12 1379  ax-bnd 1380  ax-4 1381  ax-17 1400  ax-i9 1404  ax-ial 1409  ax-i5r 1410  ax-ext 2004  ax-nul 3857
This theorem depends on definitions:  df-bi 110  df-tru 1231  df-nf 1330  df-sb 1628  df-clab 2009  df-cleq 2015  df-clel 2018  df-nfc 2149  df-v 2537  df-dif 2897  df-un 2899  df-nul 3202  df-sn 3356  df-suc 4057  df-1o 5916
This theorem is referenced by:  0lt1o  5938
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