Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  wuntp Structured version   Unicode version

Theorem wuntp 9137
 Description: A weak universe is closed under unordered triple. (Contributed by Mario Carneiro, 2-Jan-2017.)
Hypotheses
Ref Expression
wununi.1 WUni
wununi.2
wunpr.3
wuntp.3
Assertion
Ref Expression
wuntp

Proof of Theorem wuntp
StepHypRef Expression
1 tpass 4095 . 2
2 wununi.1 . . 3 WUni
3 dfsn2 4009 . . . 4
4 wununi.2 . . . . 5
52, 4, 4wunpr 9135 . . . 4
63, 5syl5eqel 2514 . . 3
7 wunpr.3 . . . 4
8 wuntp.3 . . . 4
92, 7, 8wunpr 9135 . . 3
102, 6, 9wunun 9136 . 2
111, 10syl5eqel 2514 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wcel 1868   cun 3434  csn 3996  cpr 3998  ctp 4000  WUnicwun 9126 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-5 1748  ax-6 1794  ax-7 1839  ax-10 1887  ax-11 1892  ax-12 1905  ax-13 2053  ax-ext 2400 This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372  df-3or 983  df-3an 984  df-tru 1440  df-ex 1660  df-nf 1664  df-sb 1787  df-clab 2408  df-cleq 2414  df-clel 2417  df-nfc 2572  df-ne 2620  df-ral 2780  df-rex 2781  df-v 3083  df-un 3441  df-in 3443  df-ss 3450  df-sn 3997  df-pr 3999  df-tp 4001  df-uni 4217  df-tr 4516  df-wun 9128 This theorem is referenced by:  catcfuccl  15992  catcxpccl  16080
 Copyright terms: Public domain W3C validator