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Theorem rabid2 2503
 Description: An "identity" law for restricted class abstraction. (Contributed by NM, 9-Oct-2003.) (Proof shortened by Andrew Salmon, 30-May-2011.)
Assertion
Ref Expression
rabid2
Distinct variable group:   ,
Allowed substitution hint:   ()

Proof of Theorem rabid2
StepHypRef Expression
1 abeq2 2162 . . 3
2 pm4.71 375 . . . 4
32albii 1375 . . 3
41, 3bitr4i 180 . 2
5 df-rab 2332 . . 3
65eqeq2i 2066 . 2
7 df-ral 2328 . 2
84, 6, 73bitr4i 205 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 101   wb 102  wal 1257   wceq 1259   wcel 1409  cab 2042  wral 2323  crab 2327 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-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-11 1413  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-nf 1366  df-sb 1662  df-clab 2043  df-cleq 2049  df-clel 2052  df-ral 2328  df-rab 2332 This theorem is referenced by:  rabxmdc  3277  rabrsndc  3466  class2seteq  3944  dmmptg  4846  fneqeql  5303  fmpt  5347  acexmidlemph  5533  ioomax  8918  iccmax  8919
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