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Theorem reseq1i 4551
Description: Equality inference for restrictions. (Contributed by NM, 21-Oct-2014.)
Hypothesis
Ref Expression
reseqi.1 A = B
Assertion
Ref Expression
reseq1i (A𝐶) = (B𝐶)

Proof of Theorem reseq1i
StepHypRef Expression
1 reseqi.1 . 2 A = B
2 reseq1 4549 . 2 (A = B → (A𝐶) = (B𝐶))
31, 2ax-mp 7 1 (A𝐶) = (B𝐶)
Colors of variables: wff set class
Syntax hints:   = wceq 1242  cres 4290
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bnd 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-v 2553  df-in 2918  df-res 4300
This theorem is referenced by:  reseq12i  4553  resmpt  4599  resmpt3  4600  opabresid  4602  rescnvcnv  4726  coires1  4781  fcoi1  5013  fvsnun1  5303  fvsnun2  5304  resoprab  5539  resmpt2  5541  ofmres  5705  f1stres  5728  f2ndres  5729  df1st2  5782  df2nd2  5783  dftpos2  5817  tfr2a  5877  frecsuclem1  5926  frecsuclem2  5928  divfnzn  8332
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