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Theorem reseq12i 5980
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 5978 . 2 (𝐴𝐶) = (𝐵𝐶)
3 reseqi.2 . . 3 𝐶 = 𝐷
43reseq2i 5979 . 2 (𝐵𝐶) = (𝐵𝐷)
52, 4eqtri 2761 1 (𝐴𝐶) = (𝐵𝐷)
Colors of variables: wff setvar class
Syntax hints:   = wceq 1542  cres 5679
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 3434  df-in 3956  df-opab 5212  df-xp 5683  df-res 5689
This theorem is referenced by:  cnvresid  6628  fprlem1  8285  wfrlem5OLD  8313  dfoi  9506  frrlem15  9752  lubfval  18303  glbfval  18316  odulub  18360  oduglb  18362  dvlog  26159  dvlog2  26161  issubgr  28528  finsumvtxdg2size  28807  sitgclg  33341  fourierdlem57  44879  fourierdlem74  44896  fourierdlem75  44897
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