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Theorem univ 4581
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 3842 . . 3  |-  ~P _V  =  _V
21unieqi 3853 . 2  |-  U. ~P _V  =  U. _V
3 unipw 4240 . 2  |-  U. ~P _V  =  _V
42, 3eqtr3i 2318 1  |-  U. _V  =  _V
Colors of variables: wff set class
Syntax hints:    = wceq 1632   _Vcvv 2801   ~Pcpw 3638   U.cuni 3843
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-14 1700  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277  ax-sep 4157  ax-nul 4165  ax-pr 4230
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-ne 2461  df-rex 2562  df-v 2803  df-dif 3168  df-un 3170  df-in 3172  df-ss 3179  df-nul 3469  df-pw 3640  df-sn 3659  df-pr 3660  df-uni 3844
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