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Theorem intv 4098
Description: The intersection of the universal class is empty. (Contributed by NM, 11-Sep-2008.)
Assertion
Ref Expression
intv  |-  |^| _V  =  (/)

Proof of Theorem intv
StepHypRef Expression
1 0ex 4059 . 2  |-  (/)  e.  _V
2 int0el 3805 . 2  |-  ( (/)  e.  _V  ->  |^| _V  =  (/) )
31, 2ax-mp 5 1  |-  |^| _V  =  (/)
Colors of variables: wff set class
Syntax hints:    = wceq 1332    e. wcel 1481   _Vcvv 2687   (/)c0 3364   |^|cint 3775
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 604  ax-in2 605  ax-io 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-10 1484  ax-11 1485  ax-i12 1486  ax-bndl 1487  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122  ax-nul 4058
This theorem depends on definitions:  df-bi 116  df-tru 1335  df-nf 1438  df-sb 1737  df-clab 2127  df-cleq 2133  df-clel 2136  df-nfc 2271  df-v 2689  df-dif 3074  df-in 3078  df-ss 3085  df-nul 3365  df-int 3776
This theorem is referenced by: (None)
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