Theorem reseq2i 4957

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 4955	. 2 |- ( A = B -> ( C |` A ) = ( C |` B ) )
3	1, 2	ax-mp 5	1 |- ( C |` A ) = ( C |` B )

Syntax hints:   = wceq 1373   |` cres 4678

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 711  ax-5 1470  ax-7 1471  ax-gen 1472  ax-ie1 1516  ax-ie2 1517  ax-8 1527  ax-10 1528  ax-11 1529  ax-i12 1530  ax-bndl 1532  ax-4 1533  ax-17 1549  ax-i9 1553  ax-ial 1557  ax-i5r 1558  ax-ext 2187

This theorem depends on definitions:  df-bi 117  df-tru 1376  df-nf 1484  df-sb 1786  df-clab 2192  df-cleq 2198  df-clel 2201  df-nfc 2337  df-v 2774  df-in 3172  df-opab 4107  df-xp 4682  df-res 4688

This theorem is referenced by:  reseq12i  4958  rescom  4985  resdmdfsn  5003  rescnvcnv  5146  resdm2  5174  funcnvres  5348  funimaexg  5359  resdif  5546  frecfnom  6489  facnn  10874  fac0  10875  expcnv  11848  setsslid  12916  uptx  14779  txcn  14780