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Theorem dftr3 4299
 Description: An alternate way of defining a transitive class. Definition 7.1 of [TakeutiZaring] p. 35. (Contributed by NM, 29-Aug-1993.)
Assertion
Ref Expression
dftr3
Distinct variable group:   ,

Proof of Theorem dftr3
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 dftr5 4298 . 2
2 dfss3 3331 . . 3
32ralbii 2722 . 2
41, 3bitr4i 244 1
 Colors of variables: wff set class Syntax hints:   wb 177   wcel 1725  wral 2698   wss 3313   wtr 4295 This theorem is referenced by:  trss  4304  trin  4305  triun  4308  trint  4310  tron  4597  ssorduni  4759  suceloni  4786  ordtypelem2  7481  tcwf  7800  itunitc  8294  wunex2  8606  wfgru  8684 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ral 2703  df-v 2951  df-in 3320  df-ss 3327  df-uni 4009  df-tr 4296
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