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Theorem dftr3 4549
 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 4548 . 2
2 dfss3 3493 . . 3
32ralbii 2888 . 2
41, 3bitr4i 252 1
 Colors of variables: wff setvar class Syntax hints:  <->wb 184  e.wcel 1818  A.wral 2807  C_wss 3475  Trwtr 4545 This theorem is referenced by:  trss  4554  trin  4555  triun  4558  trint  4560  tron  4906  ssorduni  6621  suceloni  6648  ordtypelem2  7965  tcwf  8322  itunitc  8822  wunex2  9137  wfgru  9215 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-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-tr 4546
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