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Theorem elpwun 6615
 Description: Membership in the power class of a union. (Contributed by NM, 26-Mar-2007.)
Hypothesis
Ref Expression
eldifpw.1
Assertion
Ref Expression
elpwun

Proof of Theorem elpwun
StepHypRef Expression
1 elex 3090 . 2
2 elex 3090 . . 3
3 eldifpw.1 . . . 4
4 difex2 6609 . . . 4
53, 4ax-mp 5 . . 3
62, 5sylibr 215 . 2
7 elpwg 3987 . . 3
8 difexg 4569 . . . . 5
9 elpwg 3987 . . . . 5
108, 9syl 17 . . . 4
11 uncom 3610 . . . . . 6
1211sseq2i 3489 . . . . 5
13 ssundif 3879 . . . . 5
1412, 13bitri 252 . . . 4
1510, 14syl6rbbr 267 . . 3
167, 15bitrd 256 . 2
171, 6, 16pm5.21nii 354 1
 Colors of variables: wff setvar class Syntax hints:   wb 187   wcel 1868  cvv 3081   cdif 3433   cun 3434   wss 3436  cpw 3979 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-5 1748  ax-6 1794  ax-7 1839  ax-8 1870  ax-9 1872  ax-10 1887  ax-11 1892  ax-12 1905  ax-13 2053  ax-ext 2400  ax-sep 4543  ax-nul 4552  ax-pr 4657  ax-un 6594 This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372  df-tru 1440  df-ex 1660  df-nf 1664  df-sb 1787  df-clab 2408  df-cleq 2414  df-clel 2417  df-nfc 2572  df-ne 2620  df-ral 2780  df-rex 2781  df-rab 2784  df-v 3083  df-dif 3439  df-un 3441  df-in 3443  df-ss 3450  df-nul 3762  df-pw 3981  df-sn 3997  df-pr 3999  df-uni 4217 This theorem is referenced by:  pwfilem  7871  elrfi  35455
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