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Theorem univ 4434
 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

Proof of Theorem univ
StepHypRef Expression
1 pwv 3771 . . 3
21unieqi 3782 . 2
3 unipw 4176 . 2
42, 3eqtr3i 2180 1
 Colors of variables: wff set class Syntax hints:   wceq 1335  cvv 2712  cpw 3543  cuni 3772 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1427  ax-7 1428  ax-gen 1429  ax-ie1 1473  ax-ie2 1474  ax-8 1484  ax-10 1485  ax-11 1486  ax-i12 1487  ax-bndl 1489  ax-4 1490  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-14 2131  ax-ext 2139  ax-sep 4082  ax-pow 4134 This theorem depends on definitions:  df-bi 116  df-tru 1338  df-nf 1441  df-sb 1743  df-clab 2144  df-cleq 2150  df-clel 2153  df-nfc 2288  df-rex 2441  df-v 2714  df-in 3108  df-ss 3115  df-pw 3545  df-sn 3566  df-uni 3773 This theorem is referenced by: (None)
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