Theorem reseq1i 4626

Description: Equality inference for restrictions. (Contributed by NM, 21-Oct-2014.)

Hypothesis

Ref	Expression
reseqi.1	|- A = B

Assertion

Ref	Expression
reseq1i	|- ( A |` C ) = ( B |` C )

Proof of Theorem reseq1i

Step	Hyp	Ref	Expression
1		reseqi.1	. 2 |- A = B
2		reseq1 4624	. 2 |- ( A = B -> ( A |` C ) = ( B |` C ) )
3	1, 2	ax-mp 7	1 |- ( A |` C ) = ( B |` C )

Syntax hints:   = wceq 1284   |` cres 4365

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 662  ax-5 1376  ax-7 1377  ax-gen 1378  ax-ie1 1422  ax-ie2 1423  ax-8 1435  ax-10 1436  ax-11 1437  ax-i12 1438  ax-bndl 1439  ax-4 1440  ax-17 1459  ax-i9 1463  ax-ial 1467  ax-i5r 1468  ax-ext 2063

This theorem depends on definitions:  df-bi 115  df-tru 1287  df-nf 1390  df-sb 1686  df-clab 2068  df-cleq 2074  df-clel 2077  df-nfc 2208  df-v 2603  df-in 2979  df-res 4375

This theorem is referenced by:  reseq12i  4628  resindm  4670  resmpt  4676  resmpt3  4677  opabresid  4679  rescnvcnv  4803  coires1  4858  fcoi1  5090  fvsnun1  5381  fvsnun2  5382  resoprab  5617  resmpt2  5619  ofmres  5783  f1stres  5806  f2ndres  5807  df1st2  5860  df2nd2  5861  dftpos2  5899  tfr2a  5959  frecsuclem1  6010  frecsuclem2  6012  divfnzn  8706