Theorem reseq2i 4657

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 4655	. 2 |- ( A = B -> ( C |` A ) = ( C |` B ) )
3	1, 2	ax-mp 7	1 |- ( C |` A ) = ( C |` B )

Syntax hints:   = wceq 1285   |` cres 4393

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 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2065

This theorem depends on definitions:  df-bi 115  df-tru 1288  df-nf 1391  df-sb 1688  df-clab 2070  df-cleq 2076  df-clel 2079  df-nfc 2212  df-v 2612  df-in 2988  df-opab 3860  df-xp 4397  df-res 4403

This theorem is referenced by:  reseq12i  4658  rescom  4684  resdmdfsn  4701  rescnvcnv  4833  resdm2  4861  funcnvres  5023  funimaexg  5034  resdif  5200  frecfnom  6071  facnn  9821  fac0  9822