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Theorem ineq2d 3272
Description: Equality deduction for intersection of two classes. (Contributed by NM, 10-Apr-1994.)
Hypothesis
Ref Expression
ineq1d.1  |-  ( ph  ->  A  =  B )
Assertion
Ref Expression
ineq2d  |-  ( ph  ->  ( C  i^i  A
)  =  ( C  i^i  B ) )

Proof of Theorem ineq2d
StepHypRef Expression
1 ineq1d.1 . 2  |-  ( ph  ->  A  =  B )
2 ineq2 3266 . 2  |-  ( A  =  B  ->  ( C  i^i  A )  =  ( C  i^i  B
) )
31, 2syl 14 1  |-  ( ph  ->  ( C  i^i  A
)  =  ( C  i^i  B ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1331    i^i cin 3065
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 2119
This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2124  df-cleq 2130  df-clel 2133  df-nfc 2268  df-v 2683  df-in 3072
This theorem is referenced by:  disjpr2  3582  rint0  3805  riin0  3879  disji2  3917  xpriindim  4672  riinint  4795  reseq2  4809  csbresg  4817  resindm  4856  isoselem  5714  zfz1isolem1  10576  fsumm1  11178  ennnfonelemhf1o  11915  restval  12115  basis1  12203  baspartn  12206  eltg  12210  tgdom  12230  ntrval  12268  resttopon2  12336  restopnb  12339  qtopbasss  12679
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