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Theorem iswun 8571
 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 4300 . . 3
2 neeq1 2606 . . 3
3 eleq2 2496 . . . . 5
4 eleq2 2496 . . . . 5
5 eleq2 2496 . . . . . 6
65raleqbi1dv 2904 . . . . 5
73, 4, 63anbi123d 1254 . . . 4
87raleqbi1dv 2904 . . 3
91, 2, 83anbi123d 1254 . 2
10 df-wun 8569 . 2 WUni
119, 10elab2g 3076 1 WUni
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   w3a 936   wceq 1652   wcel 1725   wne 2598  wral 2697  c0 3620  cpw 3791  cpr 3807  cuni 4007   wtr 4294  WUnicwun 8567 This theorem is referenced by:  wuntr  8572  wununi  8573  wunpw  8574  wunpr  8576  wun0  8585  intwun  8602  r1limwun  8603  wunex2  8605  tskwun  8651  gruwun  8680 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ne 2600  df-ral 2702  df-rex 2703  df-v 2950  df-in 3319  df-ss 3326  df-uni 4008  df-tr 4295  df-wun 8569
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