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Theorem el1o 5959
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 5952 . . 3 1𝑜 = {∅}
21eleq2i 2101 . 2 (A 1𝑜A {∅})
3 0ex 3875 . . 3 V
43elsnc2 3397 . 2 (A {∅} ↔ A = ∅)
52, 4bitri 173 1 (A 1𝑜A = ∅)
Colors of variables: wff set class
Syntax hints:  wb 98   = wceq 1242   wcel 1390  c0 3218  {csn 3367  1𝑜c1o 5933
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 544  ax-in2 545  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bnd 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019  ax-nul 3874
This theorem depends on definitions:  df-bi 110  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-v 2553  df-dif 2914  df-un 2916  df-nul 3219  df-sn 3373  df-suc 4074  df-1o 5940
This theorem is referenced by:  0lt1o  5962
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