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Theorem univ 4840
 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 4365 . . 3 𝒫 V = V
21unieqi 4375 . 2 𝒫 V = V
3 unipw 4839 . 2 𝒫 V = V
42, 3eqtr3i 2633 1 V = V
 Colors of variables: wff setvar class Syntax hints:   = wceq 1474  Vcvv 3172  𝒫 cpw 4107  ∪ cuni 4366 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1712  ax-4 1727  ax-5 1826  ax-6 1874  ax-7 1921  ax-9 1985  ax-10 2005  ax-11 2020  ax-12 2033  ax-13 2233  ax-ext 2589  ax-sep 4703  ax-nul 4712  ax-pr 4828 This theorem depends on definitions:  df-bi 195  df-or 383  df-an 384  df-3an 1032  df-tru 1477  df-ex 1695  df-nf 1700  df-sb 1867  df-clab 2596  df-cleq 2602  df-clel 2605  df-nfc 2739  df-rex 2901  df-v 3174  df-dif 3542  df-un 3544  df-in 3546  df-ss 3553  df-nul 3874  df-pw 4109  df-sn 4125  df-pr 4127  df-uni 4367 This theorem is referenced by: (None)
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