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Theorem univ 4565
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 3826 . . 3  |-  ~P _V  =  _V
21unieqi 3837 . 2  |-  U. ~P _V  =  U. _V
3 unipw 4224 . 2  |-  U. ~P _V  =  _V
42, 3eqtr3i 2305 1  |-  U. _V  =  _V
Colors of variables: wff set class
Syntax hints:    = wceq 1623   _Vcvv 2788   ~Pcpw 3625   U.cuni 3827
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-14 1688  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264  ax-sep 4141  ax-nul 4149  ax-pr 4214
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-rex 2549  df-v 2790  df-dif 3155  df-un 3157  df-in 3159  df-ss 3166  df-nul 3456  df-pw 3627  df-sn 3646  df-pr 3647  df-uni 3828
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