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Theorem reseq2d 4660
Description: Equality deduction for restrictions. (Contributed by Paul Chapman, 22-Jun-2011.)
Hypothesis
Ref Expression
reseqd.1  |-  ( ph  ->  A  =  B )
Assertion
Ref Expression
reseq2d  |-  ( ph  ->  ( C  |`  A )  =  ( C  |`  B ) )

Proof of Theorem reseq2d
StepHypRef Expression
1 reseqd.1 . 2  |-  ( ph  ->  A  =  B )
2 reseq2 4655 . 2  |-  ( A  =  B  ->  ( C  |`  A )  =  ( C  |`  B ) )
31, 2syl 14 1  |-  ( ph  ->  ( C  |`  A )  =  ( C  |`  B ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1285    |` cres 4393
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 2612  df-in 2988  df-opab 3860  df-xp 4397  df-res 4403
This theorem is referenced by:  reseq12d  4661  resima2  4692  relresfld  4897  f1orescnv  5193  funcocnv2  5202  fococnv2  5203  fnressn  5401  oprssov  5693  dftpos2  5930  dif1en  6435  fseq1p1m1  9239
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