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Theorem truni 4559
Description: The union of a class of transitive sets is transitive. Exercise 5(a) of [Enderton] p. 73. (Contributed by Scott Fenton, 21-Feb-2011.) (Proof shortened by Mario Carneiro, 26-Apr-2014.)
Assertion
Ref Expression
truni
Distinct variable group:   ,

Proof of Theorem truni
StepHypRef Expression
1 triun 4558 . 2
2 uniiun 4383 . . 3
3 treq 4551 . . 3
42, 3ax-mp 5 . 2
51, 4sylibr 212 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  <->wb 184  =wceq 1395  A.wral 2807  U.cuni 4249  U_ciun 4330  Trwtr 4545
This theorem is referenced by:  dfon2lem1  29215
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-rex 2813  df-v 3111  df-in 3482  df-ss 3489  df-uni 4250  df-iun 4332  df-tr 4546
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