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Theorem elpwuni 4418
 Description: Relationship for power class and union. (Contributed by NM, 18-Jul-2006.)
Assertion
Ref Expression
elpwuni

Proof of Theorem elpwuni
StepHypRef Expression
1 sspwuni 4416 . 2
2 unissel 4280 . . . 4
32expcom 435 . . 3
4 eqimss 3555 . . 3
53, 4impbid1 203 . 2
61, 5syl5bb 257 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  <->wb 184  =wceq 1395  e.wcel 1818  C_wss 3475  ~Pcpw 4012  U.cuni 4249 This theorem is referenced by:  mreuni  14997  ustuni  20729  utopbas  20738  issgon  28123  br2base  28240 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435 This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ral 2812  df-v 3111  df-in 3482  df-ss 3489  df-pw 4014  df-uni 4250
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