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Theorem inteqi 3778
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 3777 . 2  |-  ( A  =  B  ->  |^| A  =  |^| B )
31, 2ax-mp 5 1  |-  |^| A  =  |^| B
Colors of variables: wff set class
Syntax hints:    = wceq 1331   |^|cint 3774
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121
This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-ral 2421  df-int 3775
This theorem is referenced by:  elintrab  3786  ssintrab  3797  intmin2  3800  intsng  3808  intexrabim  4081  op1stb  4402  bm2.5ii  4415  dfiin3g  4800  op2ndb  5025  bj-dfom  13275  bj-omind  13276
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