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Theorem inteqi 3660
Description: Equality inference for class intersection. (Contributed by NM, 2-Sep-2003.)
Hypothesis
Ref Expression
inteqi.1  |-  A  =  B
Assertion
Ref Expression
inteqi  |-  |^| A  =  |^| B

Proof of Theorem inteqi
StepHypRef Expression
1 inteqi.1 . 2  |-  A  =  B
2 inteq 3659 . 2  |-  ( A  =  B  ->  |^| A  =  |^| B )
31, 2ax-mp 7 1  |-  |^| A  =  |^| B
Colors of variables: wff set class
Syntax hints:    = wceq 1285   |^|cint 3656
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2065
This theorem depends on definitions:  df-bi 115  df-tru 1288  df-nf 1391  df-sb 1688  df-clab 2070  df-cleq 2076  df-clel 2079  df-nfc 2212  df-ral 2358  df-int 3657
This theorem is referenced by:  elintrab  3668  ssintrab  3679  intmin2  3682  intsng  3690  intexrabim  3948  op1stb  4255  bm2.5ii  4268  dfiin3g  4638  op2ndb  4854  bj-dfom  10995  bj-omind  10996
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