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Theorem univ 4502
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 3767 . . 3  |-  ~P _V  =  _V
21unieqi 3778 . 2  |-  U. ~P _V  =  U. _V
3 unipw 4162 . 2  |-  U. ~P _V  =  _V
42, 3eqtr3i 2278 1  |-  U. _V  =  _V
Colors of variables: wff set class
Syntax hints:    = wceq 1619   _Vcvv 2740   ~Pcpw 3566   U.cuni 3768
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-7 1535  ax-gen 1536  ax-8 1623  ax-11 1624  ax-14 1626  ax-17 1628  ax-12o 1664  ax-10 1678  ax-9 1684  ax-4 1692  ax-16 1927  ax-ext 2237  ax-sep 4081  ax-nul 4089  ax-pr 4152
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1315  df-ex 1538  df-nf 1540  df-sb 1884  df-clab 2243  df-cleq 2249  df-clel 2252  df-nfc 2381  df-ne 2421  df-rex 2521  df-v 2742  df-dif 3097  df-un 3099  df-in 3101  df-ss 3108  df-nul 3398  df-pw 3568  df-sn 3587  df-pr 3588  df-uni 3769
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