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Theorem reseq12i 5107
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 5105 . 2  |-  ( A  |`  C )  =  ( B  |`  C )
3 reseqi.2 . . 3  |-  C  =  D
43reseq2i 5106 . 2  |-  ( B  |`  C )  =  ( B  |`  D )
52, 4eqtri 2462 1  |-  ( A  |`  C )  =  ( B  |`  D )
Colors of variables: wff setvar class
Syntax hints:    = wceq 1369    |` cres 4841
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1591  ax-4 1602  ax-5 1670  ax-6 1708  ax-7 1728  ax-10 1775  ax-11 1780  ax-12 1792  ax-13 1943  ax-ext 2423
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1372  df-ex 1587  df-nf 1590  df-sb 1701  df-clab 2429  df-cleq 2435  df-clel 2438  df-nfc 2567  df-v 2973  df-in 3334  df-opab 4350  df-xp 4845  df-res 4851
This theorem is referenced by:  cnvresid  5487  dfoi  7724  lubfval  15147  glbfval  15160  oduglb  15308  odulub  15310  dvlog  22095  dvlog2  22097  sitgclg  26727  wfrlem5  27727  frrlem5  27771
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