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Theorem ineq2i 3171
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 3168 . 2  |-  ( A  =  B  ->  ( C  i^i  A )  =  ( C  i^i  B
) )
31, 2ax-mp 7 1  |-  ( C  i^i  A )  =  ( C  i^i  B
)
Colors of variables: wff set class
Syntax hints:    = wceq 1285    i^i cin 2973
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 2064
This theorem depends on definitions:  df-bi 115  df-tru 1288  df-nf 1391  df-sb 1687  df-clab 2069  df-cleq 2075  df-clel 2078  df-nfc 2209  df-v 2604  df-in 2980
This theorem is referenced by:  in4  3189  inindir  3191  indif2  3215  difun1  3231  dfrab3ss  3249  dfif3  3372  intunsn  3682  rint0  3683  riin0  3757  res0  4644  resres  4652  resundi  4653  resindi  4655  inres  4657  resiun2  4659  resopab  4682  dfse2  4728  dminxp  4795  imainrect  4796  resdmres  4842  funimacnv  5006  unfiin  6444  dmaddpi  6577  dmmulpi  6578
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