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Theorem wunpr 9108
Description: A weak universe is closed under pairing. (Contributed by Mario Carneiro, 2-Jan-2017.)
Hypotheses
Ref Expression
wununi.1
wununi.2
wunpr.3
Assertion
Ref Expression
wunpr

Proof of Theorem wunpr
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 wununi.2 . 2
2 wunpr.3 . 2
3 wununi.1 . . 3
4 iswun 9103 . . . . 5
54ibi 241 . . . 4
65simp3d 1010 . . 3
7 simp3 998 . . . 4
87ralimi 2850 . . 3
93, 6, 83syl 20 . 2
10 preq1 4109 . . . 4
1110eleq1d 2526 . . 3
12 preq2 4110 . . . 4
1312eleq1d 2526 . . 3
1411, 13rspc2va 3220 . 2
151, 2, 9, 14syl21anc 1227 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  /\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:  wunun  9109  wuntp  9110  wunsn  9115  wunop  9121  intwun  9134  wuncval2  9146
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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