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Theorem univ 4233
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 3608 . . 3  |-  ~P _V  =  _V
21unieqi 3619 . 2  |-  U. ~P _V  =  U. _V
3 unipw 3980 . 2  |-  U. ~P _V  =  _V
42, 3eqtr3i 2104 1  |-  U. _V  =  _V
Colors of variables: wff set class
Syntax hints:    = wceq 1285   _Vcvv 2602   ~Pcpw 3390   U.cuni 3609
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 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-14 1446  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2064  ax-sep 3904  ax-pow 3956
This theorem depends on definitions:  df-bi 115  df-tru 1288  df-nf 1391  df-sb 1687  df-clab 2069  df-cleq 2075  df-clel 2078  df-nfc 2209  df-rex 2355  df-v 2604  df-in 2980  df-ss 2987  df-pw 3392  df-sn 3412  df-uni 3610
This theorem is referenced by: (None)
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