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Theorem ineq2i 3244
Description: Equality inference for intersection of two classes. (Contributed by NM, 26-Dec-1993.)
Hypothesis
Ref Expression
ineq1i.1  |-  A  =  B
Assertion
Ref Expression
ineq2i  |-  ( C  i^i  A )  =  ( C  i^i  B
)

Proof of Theorem ineq2i
StepHypRef Expression
1 ineq1i.1 . 2  |-  A  =  B
2 ineq2 3241 . 2  |-  ( A  =  B  ->  ( C  i^i  A )  =  ( C  i^i  B
) )
31, 2ax-mp 5 1  |-  ( C  i^i  A )  =  ( C  i^i  B
)
Colors of variables: wff set class
Syntax hints:    = wceq 1316    i^i cin 3040
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 683  ax-5 1408  ax-7 1409  ax-gen 1410  ax-ie1 1454  ax-ie2 1455  ax-8 1467  ax-10 1468  ax-11 1469  ax-i12 1470  ax-bndl 1471  ax-4 1472  ax-17 1491  ax-i9 1495  ax-ial 1499  ax-i5r 1500  ax-ext 2099
This theorem depends on definitions:  df-bi 116  df-tru 1319  df-nf 1422  df-sb 1721  df-clab 2104  df-cleq 2110  df-clel 2113  df-nfc 2247  df-v 2662  df-in 3047
This theorem is referenced by:  in4  3262  inindir  3264  indif2  3290  difun1  3306  dfrab3ss  3324  dfif3  3457  intunsn  3779  rint0  3780  riin0  3854  res0  4793  resres  4801  resundi  4802  resindi  4804  inres  4806  resiun2  4809  resopab  4833  dfse2  4882  dminxp  4953  imainrect  4954  resdmres  5000  funimacnv  5169  unfiin  6782  sbthlemi5  6817  dmaddpi  7101  dmmulpi  7102  fsumiun  11214
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