Theorem reseq2i 5002

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 5000	. 2 |- ( A = B -> ( C |` A ) = ( C |` B ) )
3	1, 2	ax-mp 5	1 |- ( C |` A ) = ( C |` B )

Syntax hints:   = wceq 1395   |` cres 4721

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 714  ax-5 1493  ax-7 1494  ax-gen 1495  ax-ie1 1539  ax-ie2 1540  ax-8 1550  ax-10 1551  ax-11 1552  ax-i12 1553  ax-bndl 1555  ax-4 1556  ax-17 1572  ax-i9 1576  ax-ial 1580  ax-i5r 1581  ax-ext 2211

This theorem depends on definitions:  df-bi 117  df-tru 1398  df-nf 1507  df-sb 1809  df-clab 2216  df-cleq 2222  df-clel 2225  df-nfc 2361  df-v 2801  df-in 3203  df-opab 4146  df-xp 4725  df-res 4731

This theorem is referenced by:  reseq12i  5003  rescom  5030  resdmdfsn  5048  rescnvcnv  5191  resdm2  5219  funcnvres  5394  funimaexg  5405  resdif  5594  frecfnom  6547  facnn  10949  fac0  10950  expcnv  12015  setsslid  13083  uptx  14948  txcn  14949