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Theorem wunss 9111
Description: A weak universe is closed under subsets. (Contributed by Mario Carneiro, 2-Jan-2017.)
Hypotheses
Ref Expression
wununi.1
wununi.2
wunss.3
Assertion
Ref Expression
wunss

Proof of Theorem wunss
StepHypRef Expression
1 wununi.1 . . 3
2 wununi.2 . . . 4
31, 2wunpw 9106 . . 3
41, 3wunelss 9107 . 2
5 wunss.3 . . 3
6 elpw2g 4615 . . . 4
72, 6syl 16 . . 3
85, 7mpbird 232 . 2
94, 8sseldd 3504 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  <->wb 184  e.wcel 1818  C_wss 3475  ~Pcpw 4012   cwun 9099
This theorem is referenced by:  wunin  9112  wundif  9113  wunint  9114  wun0  9117  wunom  9119  wunxp  9123  wunpm  9124  wunmap  9125  wundm  9127  wunrn  9128  wuncnv  9129  wunres  9130  wunfv  9131  wunco  9132  wuntpos  9133  wuncn  9568  wunndx  14648  wunstr  14651  wunfunc  15268
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  ax-sep 4573
This theorem depends on definitions:  df-bi 185  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-in 3482  df-ss 3489  df-pw 4014  df-uni 4250  df-tr 4546  df-wun 9101
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