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Theorem truni 4024
 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 4023 . 2
2 uniiun 3853 . . 3
3 treq 4016 . . 3
42, 3ax-mp 10 . 2
51, 4sylibr 205 1
 Colors of variables: wff set class Syntax hints:   wi 6   wb 178   wceq 1619  wral 2509  cuni 3727  ciun 3803   wtr 4010 This theorem is referenced by:  dfon2lem1  23307 This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-7 1535  ax-gen 1536  ax-8 1623  ax-11 1624  ax-17 1628  ax-12o 1664  ax-10 1678  ax-9 1684  ax-4 1692  ax-16 1926  ax-ext 2234 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1315  df-ex 1538  df-nf 1540  df-sb 1883  df-clab 2240  df-cleq 2246  df-clel 2249  df-nfc 2374  df-ral 2513  df-rex 2514  df-v 2729  df-in 3085  df-ss 3089  df-uni 3728  df-iun 3805  df-tr 4011
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