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Theorem inton 4449
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 4445 . 2  |-  (/)  e.  On
2 int0el 3893 . 2  |-  ( (/)  e.  On  ->  |^| On  =  (/) )
31, 2ax-mp 8 1  |-  |^| On  =  (/)
Colors of variables: wff set class
Syntax hints:    = wceq 1623    e. wcel 1684   (/)c0 3455   |^|cint 3862   Oncon0 4392
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264  ax-nul 4149
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-ne 2448  df-ral 2548  df-rex 2549  df-rab 2552  df-v 2790  df-dif 3155  df-in 3159  df-ss 3166  df-nul 3456  df-pw 3627  df-uni 3828  df-int 3863  df-tr 4114  df-po 4314  df-so 4315  df-fr 4352  df-we 4354  df-ord 4395  df-on 4396
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