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Theorem ineq2i 3242
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 3239 . 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 1314    i^i cin 3038
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 681  ax-5 1406  ax-7 1407  ax-gen 1408  ax-ie1 1452  ax-ie2 1453  ax-8 1465  ax-10 1466  ax-11 1467  ax-i12 1468  ax-bndl 1469  ax-4 1470  ax-17 1489  ax-i9 1493  ax-ial 1497  ax-i5r 1498  ax-ext 2097
This theorem depends on definitions:  df-bi 116  df-tru 1317  df-nf 1420  df-sb 1719  df-clab 2102  df-cleq 2108  df-clel 2111  df-nfc 2245  df-v 2660  df-in 3045
This theorem is referenced by:  in4  3260  inindir  3262  indif2  3288  difun1  3304  dfrab3ss  3322  dfif3  3455  intunsn  3777  rint0  3778  riin0  3852  res0  4791  resres  4799  resundi  4800  resindi  4802  inres  4804  resiun2  4807  resopab  4831  dfse2  4880  dminxp  4951  imainrect  4952  resdmres  4998  funimacnv  5167  unfiin  6780  sbthlemi5  6815  dmaddpi  7097  dmmulpi  7098  fsumiun  11186
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