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Theorem inton 4630
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 4626 . 2  |-  (/)  e.  On
2 int0el 4073 . 2  |-  ( (/)  e.  On  ->  |^| On  =  (/) )
31, 2ax-mp 8 1  |-  |^| On  =  (/)
Colors of variables: wff set class
Syntax hints:    = wceq 1652    e. wcel 1725   (/)c0 3620   |^|cint 4042   Oncon0 4573
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416  ax-nul 4330
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ne 2600  df-ral 2702  df-rex 2703  df-rab 2706  df-v 2950  df-dif 3315  df-in 3319  df-ss 3326  df-nul 3621  df-pw 3793  df-uni 4008  df-int 4043  df-tr 4295  df-po 4495  df-so 4496  df-fr 4533  df-we 4535  df-ord 4576  df-on 4577
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