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Theorem reseq12i 5839
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 5837 . 2 (𝐴𝐶) = (𝐵𝐶)
3 reseqi.2 . . 3 𝐶 = 𝐷
43reseq2i 5838 . 2 (𝐵𝐶) = (𝐵𝐷)
52, 4eqtri 2847 1 (𝐴𝐶) = (𝐵𝐷)
Colors of variables: wff setvar class
Syntax hints:   = wceq 1538  cres 5545
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1971  ax-7 2016  ax-8 2117  ax-9 2125  ax-12 2179  ax-ext 2796
This theorem depends on definitions:  df-bi 210  df-an 400  df-tru 1541  df-ex 1782  df-nf 1786  df-sb 2071  df-clab 2803  df-cleq 2817  df-clel 2896  df-rab 3142  df-in 3926  df-opab 5116  df-xp 5549  df-res 5555
This theorem is referenced by:  cnvresid  6422  wfrlem5  7951  dfoi  8968  lubfval  17586  glbfval  17599  oduglb  17747  odulub  17749  dvlog  25240  dvlog2  25242  issubgr  27059  finsumvtxdg2size  27338  sitgclg  31627  fprlem1  33164  frrlem15  33169  fourierdlem57  42671  fourierdlem74  42688  fourierdlem75  42689
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