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Theorem 1n0 6197
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 6194 . 2  |-  1o  =  { (/) }
2 0ex 3966 . . 3  |-  (/)  e.  _V
32snnz 3559 . 2  |-  { (/) }  =/=  (/)
41, 3eqnetri 2278 1  |-  1o  =/=  (/)
Colors of variables: wff set class
Syntax hints:    =/= wne 2255   (/)c0 3286   {csn 3446   1oc1o 6174
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in1 579  ax-in2 580  ax-io 665  ax-5 1381  ax-7 1382  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-8 1440  ax-10 1441  ax-11 1442  ax-i12 1443  ax-bndl 1444  ax-4 1445  ax-17 1464  ax-i9 1468  ax-ial 1472  ax-i5r 1473  ax-ext 2070  ax-nul 3965
This theorem depends on definitions:  df-bi 115  df-tru 1292  df-nf 1395  df-sb 1693  df-clab 2075  df-cleq 2081  df-clel 2084  df-nfc 2217  df-ne 2256  df-v 2621  df-dif 3001  df-un 3003  df-nul 3287  df-sn 3452  df-suc 4198  df-1o 6181
This theorem is referenced by:  xp01disj  6198  djulclb  6747  djuinr  6755  djuin  6756  eldju2ndl  6763  djune  6769  updjudhf  6770  updjudhcoinrg  6772  exmidomni  6798  fodjuomnilemm  6801  fodjuomnilem0  6802  1pi  6874  peano3nninf  11897  nninfalllem1  11899  nninfall  11900  nninfsellemeq  11906  nninfsellemqall  11907
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