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Theorem reseq12i 5995
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 (𝐴𝐶) = (𝐵𝐷)

Proof of Theorem reseq12i
StepHypRef Expression
1 reseqi.1 . . 3 𝐴 = 𝐵
21reseq1i 5993 . 2 (𝐴𝐶) = (𝐵𝐶)
3 reseqi.2 . . 3 𝐶 = 𝐷
43reseq2i 5994 . 2 (𝐵𝐶) = (𝐵𝐷)
52, 4eqtri 2765 1 (𝐴𝐶) = (𝐵𝐷)
Colors of variables: wff setvar class
Syntax hints:   = wceq 1540  cres 5687
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-ext 2708
This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1543  df-ex 1780  df-sb 2065  df-clab 2715  df-cleq 2729  df-clel 2816  df-rab 3437  df-in 3958  df-opab 5206  df-xp 5691  df-res 5697
This theorem is referenced by:  cnvresid  6645  fprlem1  8325  wfrlem5OLD  8353  dfoi  9551  frrlem15  9797  lubfval  18395  glbfval  18408  odulub  18452  oduglb  18454  dvlog  26693  dvlog2  26695  issubgr  29288  finsumvtxdg2size  29568  sitgclg  34344  fourierdlem57  46178  fourierdlem74  46195  fourierdlem75  46196
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