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Theorem ineq2d 3185
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 3179 . 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 1285    i^i cin 2983
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 2065
This theorem depends on definitions:  df-bi 115  df-tru 1288  df-nf 1391  df-sb 1688  df-clab 2070  df-cleq 2076  df-clel 2079  df-nfc 2212  df-v 2614  df-in 2990
This theorem is referenced by:  disjpr2  3480  rint0  3701  riin0  3775  xpriindim  4532  riinint  4652  reseq2  4666  csbresg  4674  resindm  4711  isoselem  5538
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