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Theorem iswun 9080
 Description: Properties of a weak universe. (Contributed by Mario Carneiro, 2-Jan-2017.)
Assertion
Ref Expression
iswun WUni
Distinct variable group:   ,,
Allowed substitution hints:   (,)

Proof of Theorem iswun
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 treq 4532 . . 3
2 neeq1 2722 . . 3
3 eleq2 2514 . . . . 5
4 eleq2 2514 . . . . 5
5 eleq2 2514 . . . . . 6
65raleqbi1dv 3046 . . . . 5
73, 4, 63anbi123d 1298 . . . 4
87raleqbi1dv 3046 . . 3
91, 2, 83anbi123d 1298 . 2
10 df-wun 9078 . 2 WUni
119, 10elab2g 3232 1 WUni
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 184   w3a 972   wceq 1381   wcel 1802   wne 2636  wral 2791  c0 3767  cpw 3993  cpr 4012  cuni 4230   wtr 4526  WUnicwun 9076 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1603  ax-4 1616  ax-5 1689  ax-6 1732  ax-7 1774  ax-10 1821  ax-11 1826  ax-12 1838  ax-13 1983  ax-ext 2419 This theorem depends on definitions:  df-bi 185  df-an 371  df-3an 974  df-tru 1384  df-ex 1598  df-nf 1602  df-sb 1725  df-clab 2427  df-cleq 2433  df-clel 2436  df-nfc 2591  df-ne 2638  df-ral 2796  df-rex 2797  df-v 3095  df-in 3465  df-ss 3472  df-uni 4231  df-tr 4527  df-wun 9078 This theorem is referenced by:  wuntr  9081  wununi  9082  wunpw  9083  wunpr  9085  wun0  9094  intwun  9111  r1limwun  9112  wunex2  9114  tskwun  9160  gruwun  9189  pwinfi2  37412
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