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Theorem reseq12i 4638
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 4636 . 2  |-  ( A  |`  C )  =  ( B  |`  C )
3 reseqi.2 . . 3  |-  C  =  D
43reseq2i 4637 . 2  |-  ( B  |`  C )  =  ( B  |`  D )
52, 4eqtri 2076 1  |-  ( A  |`  C )  =  ( B  |`  D )
Colors of variables: wff set class
Syntax hints:    = wceq 1259    |` cres 4375
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-io 640  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-10 1412  ax-11 1413  ax-i12 1414  ax-bndl 1415  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038
This theorem depends on definitions:  df-bi 114  df-tru 1262  df-nf 1366  df-sb 1662  df-clab 2043  df-cleq 2049  df-clel 2052  df-nfc 2183  df-v 2576  df-in 2952  df-opab 3847  df-xp 4379  df-res 4385
This theorem is referenced by:  cnvresid  5001
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