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Theorem onn0 5951
 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 5940 . 2 ∅ ∈ On
21ne0ii 4067 1 On ≠ ∅
 Colors of variables: wff setvar class Syntax hints:   ≠ wne 2933  ∅c0 4059  Oncon0 5885 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1871  ax-4 1886  ax-5 1989  ax-6 2055  ax-7 2091  ax-9 2149  ax-10 2169  ax-11 2184  ax-12 2197  ax-13 2392  ax-ext 2741  ax-nul 4942 This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-tru 1635  df-ex 1854  df-nf 1859  df-sb 2048  df-clab 2748  df-cleq 2754  df-clel 2757  df-nfc 2892  df-ne 2934  df-ral 3056  df-rex 3057  df-rab 3060  df-v 3343  df-dif 3719  df-in 3723  df-ss 3730  df-nul 4060  df-pw 4305  df-uni 4590  df-tr 4906  df-po 5188  df-so 5189  df-fr 5226  df-we 5228  df-ord 5888  df-on 5889 This theorem is referenced by:  limon  7203
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