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Theorem inton 4885
Description: The intersection of the class of ordinal numbers is the empty set. (Contributed by NM, 20-Oct-2003.)
Assertion
Ref Expression
inton  |-  |^| On  =  (/)

Proof of Theorem inton
StepHypRef Expression
1 0elon 4881 . 2  |-  (/)  e.  On
2 int0el 4268 . 2  |-  ( (/)  e.  On  ->  |^| On  =  (/) )
31, 2ax-mp 5 1  |-  |^| On  =  (/)
Colors of variables: wff setvar class
Syntax hints:    = wceq 1370    e. wcel 1758   (/)c0 3746   |^|cint 4237   Oncon0 4828
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-5 1671  ax-6 1710  ax-7 1730  ax-10 1777  ax-11 1782  ax-12 1794  ax-13 1955  ax-ext 2432  ax-nul 4530
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1373  df-ex 1588  df-nf 1591  df-sb 1703  df-clab 2440  df-cleq 2446  df-clel 2449  df-nfc 2604  df-ne 2650  df-ral 2804  df-rex 2805  df-rab 2808  df-v 3080  df-dif 3440  df-in 3444  df-ss 3451  df-nul 3747  df-pw 3971  df-uni 4201  df-int 4238  df-tr 4495  df-po 4750  df-so 4751  df-fr 4788  df-we 4790  df-ord 4831  df-on 4832
This theorem is referenced by: (None)
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