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Theorem onn0 4948
Description: The class of all ordinal numbers is not empty. (Contributed by NM, 17-Sep-1995.)
Assertion
Ref Expression
onn0  |-  On  =/=  (/)

Proof of Theorem onn0
StepHypRef Expression
1 0elon 4937 . 2  |-  (/)  e.  On
2 ne0i 3796 . 2  |-  ( (/)  e.  On  ->  On  =/=  (/) )
31, 2ax-mp 5 1  |-  On  =/=  (/)
Colors of variables: wff setvar class
Syntax hints:    e. wcel 1767    =/= wne 2662   (/)c0 3790   Oncon0 4884
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-10 1786  ax-11 1791  ax-12 1803  ax-13 1968  ax-ext 2445  ax-nul 4582
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1382  df-ex 1597  df-nf 1600  df-sb 1712  df-clab 2453  df-cleq 2459  df-clel 2462  df-nfc 2617  df-ne 2664  df-ral 2822  df-rex 2823  df-rab 2826  df-v 3120  df-dif 3484  df-in 3488  df-ss 3495  df-nul 3791  df-pw 4018  df-uni 4252  df-tr 4547  df-po 4806  df-so 4807  df-fr 4844  df-we 4846  df-ord 4887  df-on 4888
This theorem is referenced by:  limon  6666
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