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Theorem wunun 9109
 Description: A weak universe is closed under binary union. (Contributed by Mario Carneiro, 2-Jan-2017.)
Hypotheses
Ref Expression
wununi.1
wununi.2
wunpr.3
Assertion
Ref Expression
wunun

Proof of Theorem wunun
StepHypRef Expression
1 wununi.2 . . 3
2 wunpr.3 . . 3
3 uniprg 4263 . . 3
41, 2, 3syl2anc 661 . 2
5 wununi.1 . . 3
65, 1, 2wunpr 9108 . . 3
75, 6wununi 9105 . 2
84, 7eqeltrrd 2546 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  =wceq 1395  e.wcel 1818  u.cun 3473  {cpr 4031  U.cuni 4249   cwun 9099 This theorem is referenced by:  wuntp  9110  wunsuc  9116  wunfi  9120  wunxp  9123  wuntpos  9133  wunsets  14659  catcoppccl  15435 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-or 370  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-un 3480  df-in 3482  df-ss 3489  df-sn 4030  df-pr 4032  df-uni 4250  df-tr 4546  df-wun 9101
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