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Theorem reseq12i 5271
Description: Equality inference for restrictions. (Contributed by NM, 21-Oct-2014.)
Hypotheses
Ref Expression
reseqi.1  |-  A  =  B
reseqi.2  |-  C  =  D
Assertion
Ref Expression
reseq12i  |-  ( A  |`  C )  =  ( B  |`  D )

Proof of Theorem reseq12i
StepHypRef Expression
1 reseqi.1 . . 3  |-  A  =  B
21reseq1i 5269 . 2  |-  ( A  |`  C )  =  ( B  |`  C )
3 reseqi.2 . . 3  |-  C  =  D
43reseq2i 5270 . 2  |-  ( B  |`  C )  =  ( B  |`  D )
52, 4eqtri 2496 1  |-  ( A  |`  C )  =  ( B  |`  D )
Colors of variables: wff setvar class
Syntax hints:    = wceq 1379    |` cres 5001
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-10 1786  ax-11 1791  ax-12 1803  ax-13 1968  ax-ext 2445
This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1382  df-ex 1597  df-nf 1600  df-sb 1712  df-clab 2453  df-cleq 2459  df-clel 2462  df-nfc 2617  df-v 3115  df-in 3483  df-opab 4506  df-xp 5005  df-res 5011
This theorem is referenced by:  cnvresid  5658  dfoi  7936  lubfval  15465  glbfval  15478  oduglb  15626  odulub  15628  dvlog  22788  dvlog2  22790  sitgclg  27952  wfrlem5  28952  frrlem5  28996  fourierdlem57  31492  fourierdlem74  31509  fourierdlem75  31510
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