Intuitionistic Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  ILE Home  >  Th. List  >  pwuni Unicode version

Theorem pwuni 4126
 Description: A class is a subclass of the power class of its union. Exercise 6(b) of [Enderton] p. 38. (Contributed by NM, 14-Oct-1996.)
Assertion
Ref Expression
pwuni

Proof of Theorem pwuni
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 elssuni 3774 . . 3
2 vex 2694 . . . 4
32elpw 3523 . . 3
41, 3sylibr 133 . 2
54ssriv 3108 1
 Colors of variables: wff set class Syntax hints:   wcel 2112   wss 3078  cpw 3517  cuni 3746 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 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1481  ax-10 1482  ax-11 1483  ax-i12 1484  ax-bndl 1486  ax-4 1487  ax-17 1503  ax-i9 1507  ax-ial 1511  ax-i5r 1512  ax-ext 2123 This theorem depends on definitions:  df-bi 116  df-tru 1335  df-nf 1438  df-sb 1732  df-clab 2128  df-cleq 2134  df-clel 2137  df-nfc 2272  df-v 2693  df-in 3084  df-ss 3091  df-pw 3519  df-uni 3747 This theorem is referenced by:  uniexb  4405  2pwuninelg  6192  istopon  12255  eltg3i  12300  mopnfss  12691
 Copyright terms: Public domain W3C validator