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Theorem wunelss 9107
Description: The elements of a weak universe are also subsets of it. (Contributed by Mario Carneiro, 2-Jan-2017.)
Hypotheses
Ref Expression
wununi.1
wununi.2
Assertion
Ref Expression
wunelss

Proof of Theorem wunelss
StepHypRef Expression
1 wununi.1 . . 3
2 wuntr 9104 . . 3
31, 2syl 16 . 2
4 wununi.2 . 2
5 trss 4554 . 2
63, 4, 5sylc 60 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  e.wcel 1818  C_wss 3475  Trwtr 4545   cwun 9099
This theorem is referenced by:  wunss  9111  wunf  9126  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-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-uni 4250  df-tr 4546  df-wun 9101
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