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Theorem iswun 9103
 Description: Properties of a weak universe. (Contributed by Mario Carneiro, 2-Jan-2017.)
Assertion
Ref Expression
iswun
Distinct variable group:   ,,

Proof of Theorem iswun
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 treq 4551 . . 3
2 neeq1 2738 . . 3
3 eleq2 2530 . . . . 5
4 eleq2 2530 . . . . 5
5 eleq2 2530 . . . . . 6
65raleqbi1dv 3062 . . . . 5
73, 4, 63anbi123d 1299 . . . 4
87raleqbi1dv 3062 . . 3
91, 2, 83anbi123d 1299 . 2
10 df-wun 9101 . 2
119, 10elab2g 3248 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  <->wb 184  /\w3a 973  =wceq 1395  e.wcel 1818  =/=wne 2652  A.wral 2807   c0 3784  ~Pcpw 4012  {cpr 4031  U.cuni 4249  Trwtr 4545   cwun 9099 This theorem is referenced by:  wuntr  9104  wununi  9105  wunpw  9106  wunpr  9108  wun0  9117  intwun  9134  r1limwun  9135  wunex2  9137  tskwun  9183  gruwun  9212  pwinfi2  37747 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-3an 975  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-ne 2654  df-ral 2812  df-rex 2813  df-v 3111  df-in 3482  df-ss 3489  df-uni 4250  df-tr 4546  df-wun 9101
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