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Theorem onn0 4647
Description: The class of all ordinal numbers in not empty. (Contributed by NM, 17-Sep-1995.)
Assertion
Ref Expression
onn0  |-  On  =/=  (/)

Proof of Theorem onn0
StepHypRef Expression
1 0elon 4636 . 2  |-  (/)  e.  On
2 ne0i 3636 . 2  |-  ( (/)  e.  On  ->  On  =/=  (/) )
31, 2ax-mp 8 1  |-  On  =/=  (/)
Colors of variables: wff set class
Syntax hints:    e. wcel 1726    =/= wne 2601   (/)c0 3630   Oncon0 4583
This theorem is referenced by:  limon  4818
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419  ax-nul 4340
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ne 2603  df-ral 2712  df-rex 2713  df-rab 2716  df-v 2960  df-dif 3325  df-in 3329  df-ss 3336  df-nul 3631  df-pw 3803  df-uni 4018  df-tr 4305  df-po 4505  df-so 4506  df-fr 4543  df-we 4545  df-ord 4586  df-on 4587
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