Theorem reseq2i 4905

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 4903	. 2 |- ( A = B -> ( C |` A ) = ( C |` B ) )
3	1, 2	ax-mp 5	1 |- ( C |` A ) = ( C |` B )

Syntax hints:   = wceq 1353   |` cres 4629

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 709  ax-5 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-10 1505  ax-11 1506  ax-i12 1507  ax-bndl 1509  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534  ax-i5r 1535  ax-ext 2159

This theorem depends on definitions:  df-bi 117  df-tru 1356  df-nf 1461  df-sb 1763  df-clab 2164  df-cleq 2170  df-clel 2173  df-nfc 2308  df-v 2740  df-in 3136  df-opab 4066  df-xp 4633  df-res 4639

This theorem is referenced by:  reseq12i  4906  rescom  4933  resdmdfsn  4951  rescnvcnv  5092  resdm2  5120  funcnvres  5290  funimaexg  5301  resdif  5484  frecfnom  6402  facnn  10707  fac0  10708  expcnv  11512  setsslid  12513  uptx  13777  txcn  13778