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Theorem reseq12i 5315
 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 5313 . 2 (𝐴𝐶) = (𝐵𝐶)
3 reseqi.2 . . 3 𝐶 = 𝐷
43reseq2i 5314 . 2 (𝐵𝐶) = (𝐵𝐷)
52, 4eqtri 2632 1 (𝐴𝐶) = (𝐵𝐷)
 Colors of variables: wff setvar class Syntax hints:   = wceq 1475   ↾ cres 5040 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-10 2006  ax-11 2021  ax-12 2034  ax-13 2234  ax-ext 2590 This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-tru 1478  df-ex 1696  df-nf 1701  df-sb 1868  df-clab 2597  df-cleq 2603  df-clel 2606  df-nfc 2740  df-v 3175  df-in 3547  df-opab 4644  df-xp 5044  df-res 5050 This theorem is referenced by:  cnvresid  5882  wfrlem5  7306  dfoi  8299  lubfval  16801  glbfval  16814  oduglb  16962  odulub  16964  dvlog  24197  dvlog2  24199  sitgclg  29731  frrlem5  31028  fourierdlem57  39056  fourierdlem74  39073  fourierdlem75  39074  issubgr  40495
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