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Theorem truni 4072
 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 4071 . 2
2 uniiun 3898 . . 3
3 treq 4064 . . 3
42, 3ax-mp 5 . 2
51, 4sylibr 133 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 104   wceq 1332  wral 2432  cuni 3768  ciun 3845   wtr 4058 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1481  ax-10 1482  ax-11 1483  ax-i12 1484  ax-bndl 1486  ax-4 1487  ax-17 1503  ax-i9 1507  ax-ial 1511  ax-i5r 1512  ax-ext 2136 This theorem depends on definitions:  df-bi 116  df-tru 1335  df-nf 1438  df-sb 1740  df-clab 2141  df-cleq 2147  df-clel 2150  df-nfc 2285  df-ral 2437  df-rex 2438  df-v 2711  df-in 3104  df-ss 3111  df-uni 3769  df-iun 3847  df-tr 4059 This theorem is referenced by: (None)
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