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Theorem inton 4579
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 4575 . 2  |-  (/)  e.  On
2 int0el 4023 . 2  |-  ( (/)  e.  On  ->  |^| On  =  (/) )
31, 2ax-mp 8 1  |-  |^| On  =  (/)
Colors of variables: wff set class
Syntax hints:    = wceq 1649    e. wcel 1717   (/)c0 3571   |^|cint 3992   Oncon0 4522
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1661  ax-8 1682  ax-6 1736  ax-7 1741  ax-11 1753  ax-12 1939  ax-ext 2368  ax-nul 4279
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2374  df-cleq 2380  df-clel 2383  df-nfc 2512  df-ne 2552  df-ral 2654  df-rex 2655  df-rab 2658  df-v 2901  df-dif 3266  df-in 3270  df-ss 3277  df-nul 3572  df-pw 3744  df-uni 3958  df-int 3993  df-tr 4244  df-po 4444  df-so 4445  df-fr 4482  df-we 4484  df-ord 4525  df-on 4526
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