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Theorem univ 4298
Description: The union of the universe is the universe. Exercise 4.12(c) of [Mendelson] p. 235. (Contributed by NM, 14-Sep-2003.)
Assertion
Ref Expression
univ  |-  U. _V  =  _V

Proof of Theorem univ
StepHypRef Expression
1 pwv 3652 . . 3  |-  ~P _V  =  _V
21unieqi 3663 . 2  |-  U. ~P _V  =  U. _V
3 unipw 4044 . 2  |-  U. ~P _V  =  _V
42, 3eqtr3i 2110 1  |-  U. _V  =  _V
Colors of variables: wff set class
Syntax hints:    = wceq 1289   _Vcvv 2619   ~Pcpw 3429   U.cuni 3653
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 665  ax-5 1381  ax-7 1382  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-8 1440  ax-10 1441  ax-11 1442  ax-i12 1443  ax-bndl 1444  ax-4 1445  ax-14 1450  ax-17 1464  ax-i9 1468  ax-ial 1472  ax-i5r 1473  ax-ext 2070  ax-sep 3957  ax-pow 4009
This theorem depends on definitions:  df-bi 115  df-tru 1292  df-nf 1395  df-sb 1693  df-clab 2075  df-cleq 2081  df-clel 2084  df-nfc 2217  df-rex 2365  df-v 2621  df-in 3005  df-ss 3012  df-pw 3431  df-sn 3452  df-uni 3654
This theorem is referenced by: (None)
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