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Theorem ordgt0ge1 5933
Description: Two ways to express that an ordinal class is positive. (Contributed by NM, 21-Dec-2004.)
Assertion
Ref Expression
ordgt0ge1  Ord  (/)  1o  C_

Proof of Theorem ordgt0ge1
StepHypRef Expression
1 0elon 4078 . . 3  (/)  On
2 ordelsuc 4181 . . 3  (/)  On  Ord  (/)  suc  (/)  C_
31, 2mpan 402 . 2  Ord  (/)  suc  (/)  C_
4 df-1o 5916 . . 3  1o  suc  (/)
54sseq1i 2946 . 2  1o  C_  suc  (/)  C_
63, 5syl6bbr 187 1  Ord  (/)  1o  C_
Colors of variables: wff set class
Syntax hints:   wi 4   wb 98   wcel 1374    C_ wss 2894   (/)c0 3201   Ord word 4048   Oncon0 4049   suc csuc 4051   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-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:  ordge1n0im  5934  archnqq  6274
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