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Theorem pwuni 3934
 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 3599 . . 3
2 vex 2554 . . . 4
32elpw 3357 . . 3
41, 3sylibr 137 . 2
54ssriv 2943 1
 Colors of variables: wff set class Syntax hints:   wcel 1390   wss 2911  cpw 3351  cuni 3571 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bnd 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019 This theorem depends on definitions:  df-bi 110  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-v 2553  df-in 2918  df-ss 2925  df-pw 3353  df-uni 3572 This theorem is referenced by:  uniexb  4171  2pwuninelg  5839
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