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Theorem univ 4235
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 V = V

Proof of Theorem univ
StepHypRef Expression
1 pwv 3607 . . 3 𝒫 V = V
21unieqi 3618 . 2 𝒫 V = V
3 unipw 3981 . 2 𝒫 V = V
42, 3eqtr3i 2078 1 V = V
Colors of variables: wff set class
Syntax hints:   = wceq 1259  Vcvv 2574  𝒫 cpw 3387   cuni 3608
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-io 640  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-10 1412  ax-11 1413  ax-i12 1414  ax-bndl 1415  ax-4 1416  ax-14 1421  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038  ax-sep 3903  ax-pow 3955
This theorem depends on definitions:  df-bi 114  df-tru 1262  df-nf 1366  df-sb 1662  df-clab 2043  df-cleq 2049  df-clel 2052  df-nfc 2183  df-rex 2329  df-v 2576  df-in 2952  df-ss 2959  df-pw 3389  df-sn 3409  df-uni 3609
This theorem is referenced by: (None)
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