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Theorem wunpr 9141
 Description: A weak universe is closed under pairing. (Contributed by Mario Carneiro, 2-Jan-2017.)
Hypotheses
Ref Expression
wununi.1 WUni
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 WUni
4 iswun 9136 . . . . 5 WUni WUni
54ibi 244 . . . 4 WUni
65simp3d 1019 . . 3 WUni
7 simp3 1007 . . . 4
87ralimi 2815 . . 3
93, 6, 83syl 18 . 2
10 preq1 4079 . . . 4
1110eleq1d 2491 . . 3
12 preq2 4080 . . . 4
1312eleq1d 2491 . . 3
1411, 13rspc2va 3192 . 2
151, 2, 9, 14syl21anc 1263 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   w3a 982   wceq 1437   wcel 1872   wne 2614  wral 2771  c0 3761  cpw 3981  cpr 4000  cuni 4219   wtr 4518  WUnicwun 9132 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1663  ax-4 1676  ax-5 1752  ax-6 1798  ax-7 1843  ax-10 1891  ax-11 1896  ax-12 1909  ax-13 2057  ax-ext 2401 This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372  df-3an 984  df-tru 1440  df-ex 1658  df-nf 1662  df-sb 1791  df-clab 2408  df-cleq 2414  df-clel 2417  df-nfc 2568  df-ne 2616  df-ral 2776  df-rex 2777  df-v 3082  df-un 3441  df-in 3443  df-ss 3450  df-sn 3999  df-pr 4001  df-uni 4220  df-tr 4519  df-wun 9134 This theorem is referenced by:  wunun  9142  wuntp  9143  wunsn  9148  wunop  9154  intwun  9167  wuncval2  9179
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