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Theorem 1n0 6047
Description: Ordinal one is not equal to ordinal zero. (Contributed by NM, 26-Dec-2004.)
Assertion
Ref Expression
1n0 1𝑜 ≠ ∅

Proof of Theorem 1n0
StepHypRef Expression
1 df1o2 6044 . 2 1𝑜 = {∅}
2 0ex 3912 . . 3 ∅ ∈ V
32snnz 3515 . 2 {∅} ≠ ∅
41, 3eqnetri 2243 1 1𝑜 ≠ ∅
Colors of variables: wff set class
Syntax hints:  wne 2220  c0 3252  {csn 3403  1𝑜c1o 6025
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-in1 554  ax-in2 555  ax-io 640  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-10 1412  ax-11 1413  ax-i12 1414  ax-bndl 1415  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038  ax-nul 3911
This theorem depends on definitions:  df-bi 114  df-tru 1262  df-nf 1366  df-sb 1662  df-clab 2043  df-cleq 2049  df-clel 2052  df-nfc 2183  df-ne 2221  df-v 2576  df-dif 2948  df-un 2950  df-nul 3253  df-sn 3409  df-suc 4136  df-1o 6032
This theorem is referenced by:  xp01disj  6048  1pi  6471
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