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Theorem univ 4564
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 3827 . . 3  |-  ~P _V  =  _V
21unieqi 3838 . 2  |-  U. ~P _V  =  U. _V
3 unipw 4223 . 2  |-  U. ~P _V  =  _V
42, 3eqtr3i 2306 1  |-  U. _V  =  _V
Colors of variables: wff set class
Syntax hints:    = wceq 1624   _Vcvv 2789   ~Pcpw 3626   U.cuni 3828
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-gen 1534  ax-5 1545  ax-17 1604  ax-9 1637  ax-8 1645  ax-14 1689  ax-6 1704  ax-7 1709  ax-11 1716  ax-12 1867  ax-ext 2265  ax-sep 4142  ax-nul 4150  ax-pr 4213
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1312  df-ex 1530  df-nf 1533  df-sb 1632  df-clab 2271  df-cleq 2277  df-clel 2280  df-nfc 2409  df-ne 2449  df-rex 2550  df-v 2791  df-dif 3156  df-un 3158  df-in 3160  df-ss 3167  df-nul 3457  df-pw 3628  df-sn 3647  df-pr 3648  df-uni 3829
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