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Theorem 1n0 6295
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 6292 . 2  |-  1o  =  { (/) }
2 0ex 4023 . . 3  |-  (/)  e.  _V
32snnz 3610 . 2  |-  { (/) }  =/=  (/)
41, 3eqnetri 2306 1  |-  1o  =/=  (/)
Colors of variables: wff set class
Syntax hints:    =/= wne 2283   (/)c0 3331   {csn 3495   1oc1o 6272
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 586  ax-in2 587  ax-io 681  ax-5 1406  ax-7 1407  ax-gen 1408  ax-ie1 1452  ax-ie2 1453  ax-8 1465  ax-10 1466  ax-11 1467  ax-i12 1468  ax-bndl 1469  ax-4 1470  ax-17 1489  ax-i9 1493  ax-ial 1497  ax-i5r 1498  ax-ext 2097  ax-nul 4022
This theorem depends on definitions:  df-bi 116  df-tru 1317  df-nf 1420  df-sb 1719  df-clab 2102  df-cleq 2108  df-clel 2111  df-nfc 2245  df-ne 2284  df-v 2660  df-dif 3041  df-un 3043  df-nul 3332  df-sn 3501  df-suc 4261  df-1o 6279
This theorem is referenced by:  xp01disj  6296  xp01disjl  6297  djulclb  6906  djuinr  6914  eldju2ndl  6923  djune  6929  updjudhf  6930  updjudhcoinrg  6932  exmidomni  6980  fodjum  6984  fodju0  6985  ismkvnex  6995  mkvprop  6998  1pi  7087  unct  11860  pwle2  13027  subctctexmid  13030  peano3nninf  13035  nninfalllem1  13037  nninfall  13038  nninfsellemeq  13044  nninfsellemqall  13045  nninffeq  13050
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