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Theorem trint0 4507
 Description: Any nonempty transitive class includes its intersection. Exercise 2 in [TakeutiZaring] p. 44. (Contributed by Andrew Salmon, 14-Nov-2011.)
Assertion
Ref Expression
trint0

Proof of Theorem trint0
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 n0 3732 . . 3
2 intss1 4241 . . . . 5
3 trss 4499 . . . . . 6
43com12 31 . . . . 5
5 sstr2 3425 . . . . 5
62, 4, 5sylsyld 57 . . . 4
76exlimiv 1784 . . 3
81, 7sylbi 200 . 2
98impcom 437 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wa 376  wex 1671   wcel 1904   wne 2641   wss 3390  c0 3722  cint 4226   wtr 4490 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-5 1766  ax-6 1813  ax-7 1859  ax-10 1932  ax-11 1937  ax-12 1950  ax-13 2104  ax-ext 2451 This theorem depends on definitions:  df-bi 190  df-or 377  df-an 378  df-tru 1455  df-ex 1672  df-nf 1676  df-sb 1806  df-clab 2458  df-cleq 2464  df-clel 2467  df-nfc 2601  df-ne 2643  df-ral 2761  df-v 3033  df-dif 3393  df-in 3397  df-ss 3404  df-nul 3723  df-uni 4191  df-int 4227  df-tr 4491 This theorem is referenced by: (None)
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