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Theorem dftr3 3886
 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 3885 . 2
2 dfss3 2963 . . 3
32ralbii 2347 . 2
41, 3bitr4i 180 1
 Colors of variables: wff set class Syntax hints:   wb 102   wcel 1409  wral 2323   wss 2945   wtr 3882 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-io 640  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-10 1412  ax-11 1413  ax-i12 1414  ax-bndl 1415  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038 This theorem depends on definitions:  df-bi 114  df-tru 1262  df-nf 1366  df-sb 1662  df-clab 2043  df-cleq 2049  df-clel 2052  df-nfc 2183  df-ral 2328  df-v 2576  df-in 2952  df-ss 2959  df-uni 3609  df-tr 3883 This theorem is referenced by:  trss  3891  trin  3892  triun  3895  trint  3897  tron  4147  ssorduni  4241  bj-nntrans2  10464  bj-omtrans2  10469
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