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Theorem pwuni 3971
 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 3636 . . 3
2 vex 2577 . . . 4
32elpw 3393 . . 3
41, 3sylibr 141 . 2
54ssriv 2977 1
 Colors of variables: wff set class Syntax hints:   wcel 1409   wss 2945  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-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038 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-v 2576  df-in 2952  df-ss 2959  df-pw 3389  df-uni 3609 This theorem is referenced by:  uniexb  4233  2pwuninelg  5929
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