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Theorem ordge1n0im 5934
Description: An ordinal greater than or equal to 1 is nonzero. (Contributed by Jim Kingdon, 26-Jun-2019.)
Assertion
Ref Expression
ordge1n0im  Ord  1o  C_  =/=  (/)

Proof of Theorem ordge1n0im
StepHypRef Expression
1 ordgt0ge1 5933 . 2  Ord  (/)  1o  C_
2 ne0i 3207 . 2  (/)  =/=  (/)
31, 2syl6bir 153 1  Ord  1o  C_  =/=  (/)
Colors of variables: wff set class
Syntax hints:   wi 4   wcel 1374    =/= wne 2186    C_ wss 2894   (/)c0 3201   Ord word 4048   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-ne 2188  df-ral 2289  df-rex 2290  df-v 2537  df-dif 2897  df-un 2899  df-in 2901  df-ss 2908  df-nul 3202  df-pw 3336  df-sn 3356  df-uni 3555  df-tr 3829  df-iord 4052  df-on 4054  df-suc 4057  df-1o 5916
This theorem is referenced by: (None)
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