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Theorem wunpw 9115
 Description: A weak universe is closed under powerset. (Contributed by Mario Carneiro, 2-Jan-2017.)
Hypotheses
Ref Expression
wununi.1 WUni
wununi.2
Assertion
Ref Expression
wunpw

Proof of Theorem wunpw
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 wununi.2 . 2
2 wununi.1 . . 3 WUni
3 iswun 9112 . . . . 5 WUni WUni
43ibi 241 . . . 4 WUni
54simp3d 1011 . . 3 WUni
6 simp2 998 . . . 4
76ralimi 2797 . . 3
82, 5, 73syl 18 . 2
9 pweq 3958 . . . 4
109eleq1d 2471 . . 3
1110rspcv 3156 . 2
121, 8, 11sylc 59 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   w3a 974   wceq 1405   wcel 1842   wne 2598  wral 2754  c0 3738  cpw 3955  cpr 3974  cuni 4191   wtr 4489  WUnicwun 9108 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1639  ax-4 1652  ax-5 1725  ax-6 1771  ax-7 1814  ax-10 1861  ax-11 1866  ax-12 1878  ax-13 2026  ax-ext 2380 This theorem depends on definitions:  df-bi 185  df-an 369  df-3an 976  df-tru 1408  df-ex 1634  df-nf 1638  df-sb 1764  df-clab 2388  df-cleq 2394  df-clel 2397  df-nfc 2552  df-ne 2600  df-ral 2759  df-rex 2760  df-v 3061  df-in 3421  df-ss 3428  df-pw 3957  df-uni 4192  df-tr 4490  df-wun 9110 This theorem is referenced by:  wunss  9120  wunr1om  9127  wunxp  9132  wunpm  9133  intwun  9143  r1wunlim  9145  wuncval2  9155  wuncn  9577  wunfunc  15512  wunnat  15569  catcoppccl  15711  catcfuccl  15712  catcxpccl  15800
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