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Theorem reseq1i 4636
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 4634 . 2 (𝐴 = 𝐵 → (𝐴𝐶) = (𝐵𝐶))
31, 2ax-mp 7 1 (𝐴𝐶) = (𝐵𝐶)
Colors of variables: wff set class
Syntax hints:   = wceq 1259  cres 4375
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-io 640  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-10 1412  ax-11 1413  ax-i12 1414  ax-bndl 1415  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038
This theorem depends on definitions:  df-bi 114  df-tru 1262  df-nf 1366  df-sb 1662  df-clab 2043  df-cleq 2049  df-clel 2052  df-nfc 2183  df-v 2576  df-in 2952  df-res 4385
This theorem is referenced by:  reseq12i  4638  resmpt  4684  resmpt3  4685  opabresid  4687  rescnvcnv  4811  coires1  4866  fcoi1  5098  fvsnun1  5388  fvsnun2  5389  resoprab  5625  resmpt2  5627  ofmres  5791  f1stres  5814  f2ndres  5815  df1st2  5868  df2nd2  5869  dftpos2  5907  tfr2a  5967  frecsuclem1  6018  frecsuclem2  6020  divfnzn  8653
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