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Theorem inteqi 3874
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 3873 . 2  |-  ( A  =  B  ->  |^| A  =  |^| B )
31, 2ax-mp 5 1  |-  |^| A  =  |^| B
Colors of variables: wff set class
Syntax hints:    = wceq 1364   |^|cint 3870
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 710  ax-5 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-10 1516  ax-11 1517  ax-i12 1518  ax-bndl 1520  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546  ax-ext 2175
This theorem depends on definitions:  df-bi 117  df-tru 1367  df-nf 1472  df-sb 1774  df-clab 2180  df-cleq 2186  df-clel 2189  df-nfc 2325  df-ral 2477  df-int 3871
This theorem is referenced by:  elintrab  3882  ssintrab  3893  intmin2  3896  intsng  3904  intexrabim  4182  op1stb  4509  bm2.5ii  4528  dfiin3g  4920  op2ndb  5149  bj-dfom  15425  bj-omind  15426
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