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Theorem reseq12i 5939
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 5937 . 2 (𝐴𝐶) = (𝐵𝐶)
3 reseqi.2 . . 3 𝐶 = 𝐷
43reseq2i 5938 . 2 (𝐵𝐶) = (𝐵𝐷)
52, 4eqtri 2761 1 (𝐴𝐶) = (𝐵𝐷)
Colors of variables: wff setvar class
Syntax hints:   = wceq 1542  cres 5639
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-ext 2704
This theorem depends on definitions:  df-bi 206  df-an 398  df-tru 1545  df-ex 1783  df-sb 2069  df-clab 2711  df-cleq 2725  df-clel 2811  df-rab 3407  df-in 3921  df-opab 5172  df-xp 5643  df-res 5649
This theorem is referenced by:  cnvresid  6584  fprlem1  8235  wfrlem5OLD  8263  dfoi  9455  frrlem15  9701  lubfval  18247  glbfval  18260  odulub  18304  oduglb  18306  dvlog  26029  dvlog2  26031  issubgr  28268  finsumvtxdg2size  28547  sitgclg  33006  fourierdlem57  44494  fourierdlem74  44511  fourierdlem75  44512
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