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Theorem inton 4924
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 4920 . 2  |-  (/)  e.  On
2 int0el 4303 . 2  |-  ( (/)  e.  On  ->  |^| On  =  (/) )
31, 2ax-mp 5 1  |-  |^| On  =  (/)
Colors of variables: wff setvar class
Syntax hints:    = wceq 1398    e. wcel 1823   (/)c0 3783   |^|cint 4271   Oncon0 4867
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1623  ax-4 1636  ax-5 1709  ax-6 1752  ax-7 1795  ax-10 1842  ax-11 1847  ax-12 1859  ax-13 2004  ax-ext 2432  ax-nul 4568
This theorem depends on definitions:  df-bi 185  df-or 368  df-an 369  df-tru 1401  df-ex 1618  df-nf 1622  df-sb 1745  df-clab 2440  df-cleq 2446  df-clel 2449  df-nfc 2604  df-ne 2651  df-ral 2809  df-rex 2810  df-rab 2813  df-v 3108  df-dif 3464  df-in 3468  df-ss 3475  df-nul 3784  df-pw 4001  df-uni 4236  df-int 4272  df-tr 4533  df-po 4789  df-so 4790  df-fr 4827  df-we 4829  df-ord 4870  df-on 4871
This theorem is referenced by: (None)
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