Theorem reseq2i 4627

Description: Equality inference for restrictions. (Contributed by Paul Chapman, 22-Jun-2011.)

Hypothesis

Ref	Expression
reseqi.1	|- A = B

Assertion

Ref	Expression
reseq2i	|- ( C |` A ) = ( C |` B )

Proof of Theorem reseq2i

Step	Hyp	Ref	Expression
1		reseqi.1	. 2 |- A = B
2		reseq2 4625	. 2 |- ( A = B -> ( C |` A ) = ( C |` B ) )
3	1, 2	ax-mp 7	1 |- ( C |` A ) = ( C |` B )

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-opab 3840  df-xp 4369  df-res 4375

This theorem is referenced by:  reseq12i  4628  rescom  4654  resdmdfsn  4671  rescnvcnv  4803  resdm2  4831  funcnvres  4992  funimaexg  5003  resdif  5168  frecfnom  6009  facnn  9654  fac0  9655