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Theorem trint 4560
 Description: The intersection of a class of transitive sets is transitive. Exercise 5(b) of [Enderton] p. 73. (Contributed by Scott Fenton, 25-Feb-2011.)
Assertion
Ref Expression
trint
Distinct variable group:   ,

Proof of Theorem trint
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 dftr3 4549 . . . . 5
21ralbii 2888 . . . 4
3 df-ral 2812 . . . . . 6
43ralbii 2888 . . . . 5
5 ralcom4 3128 . . . . 5
64, 5bitri 249 . . . 4
72, 6sylbb 197 . . 3
8 ralim 2846 . . . 4
98alimi 1633 . . 3
107, 9syl 16 . 2
11 dftr3 4549 . . 3
12 df-ral 2812 . . . 4
13 vex 3112 . . . . . . 7
1413elint2 4293 . . . . . 6
15 ssint 4302 . . . . . 6
1614, 15imbi12i 326 . . . . 5
1716albii 1640 . . . 4
1812, 17bitri 249 . . 3
1911, 18bitri 249 . 2
2010, 19sylibr 212 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  A.wal 1393  e.wcel 1818  A.wral 2807  C_wss 3475  |^|cint 4286  Trwtr 4545 This theorem is referenced by:  tctr  8192  intwun  9134  intgru  9213  dfon2lem8  29222 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-or 370  df-an 371  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-ral 2812  df-v 3111  df-in 3482  df-ss 3489  df-uni 4250  df-int 4287  df-tr 4546
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