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Theorem unv 3254
Description: The union of a class with the universal class is the universal class. Exercise 4.10(l) of [Mendelson] p. 231. (Contributed by NM, 17-May-1998.)
Assertion
Ref Expression
unv  |-  ( A  u.  _V )  =  _V

Proof of Theorem unv
StepHypRef Expression
1 ssv 2965 . 2  |-  ( A  u.  _V )  C_  _V
2 ssun2 3107 . 2  |-  _V  C_  ( A  u.  _V )
31, 2eqssi 2961 1  |-  ( A  u.  _V )  =  _V
Colors of variables: wff set class
Syntax hints:    = wceq 1243   _Vcvv 2557    u. cun 2915
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022
This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-v 2559  df-un 2922  df-in 2924  df-ss 2931
This theorem is referenced by: (None)
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