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Theorem trint0m 3841
Description: Any inhabited transitive class includes its intersection. Similar to Exercise 2 in [TakeutiZaring] p. 44. (Contributed by Jim Kingdon, 22-Aug-2018.)
Assertion
Ref Expression
trint0m  Tr  |^|  C_
Distinct variable group:   ,

Proof of Theorem trint0m
StepHypRef Expression
1 intss1 3600 . . . 4  |^|  C_
2 trss 3833 . . . . 5  Tr  C_
32com12 27 . . . 4  Tr  C_
4 sstr2 2925 . . . 4  |^|  C_  C_  |^|  C_
51, 3, 4sylsyld 52 . . 3  Tr  |^|  C_
65exlimiv 1467 . 2  Tr  |^|  C_
76impcom 116 1  Tr  |^|  C_
Colors of variables: wff set class
Syntax hints:   wi 4   wa 97  wex 1358   wcel 1370    C_ wss 2890   |^|cint 3585   Tr wtr 3824
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 617  ax-5 1312  ax-7 1313  ax-gen 1314  ax-ie1 1359  ax-ie2 1360  ax-8 1372  ax-10 1373  ax-11 1374  ax-i12 1375  ax-bnd 1376  ax-4 1377  ax-17 1396  ax-i9 1400  ax-ial 1405  ax-i5r 1406  ax-ext 2000
This theorem depends on definitions:  df-bi 110  df-tru 1229  df-nf 1326  df-sb 1624  df-clab 2005  df-cleq 2011  df-clel 2014  df-nfc 2145  df-ral 2285  df-v 2533  df-in 2897  df-ss 2904  df-uni 3551  df-int 3586  df-tr 3825
This theorem is referenced by: (None)
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