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Theorem trintssm 3899
 Description: Any inhabited transitive class includes its intersection. Similar to Exercise 3 in [TakeutiZaring] p. 44 (which mistakenly does not include the inhabitedness hypothesis). (Contributed by Jim Kingdon, 22-Aug-2018.)
Assertion
Ref Expression
trintssm
Distinct variable group:   ,

Proof of Theorem trintssm
StepHypRef Expression
1 intss1 3659 . . . 4
2 trss 3892 . . . . 5
32com12 30 . . . 4
4 sstr2 3007 . . . 4
51, 3, 4sylsyld 57 . . 3
65exlimiv 1530 . 2
76impcom 123 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 102  wex 1422   wcel 1434   wss 2974  cint 3644   wtr 3883 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2064 This theorem depends on definitions:  df-bi 115  df-tru 1288  df-nf 1391  df-sb 1687  df-clab 2069  df-cleq 2075  df-clel 2078  df-nfc 2209  df-ral 2354  df-v 2604  df-in 2980  df-ss 2987  df-uni 3610  df-int 3645  df-tr 3884 This theorem is referenced by: (None)
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