Theorem reseq12i 4920

Description: Equality inference for restrictions. (Contributed by NM, 21-Oct-2014.)

Hypotheses

Ref	Expression
reseqi.1	|- A = B
reseqi.2	|- C = D

Assertion

Ref	Expression
reseq12i	|- ( A |` C ) = ( B |` D )

Proof of Theorem reseq12i

Step	Hyp	Ref	Expression
1		reseqi.1	. . 3 |- A = B
2	1	reseq1i 4918	. 2 |- ( A |` C ) = ( B |` C )
3		reseqi.2	. . 3 |- C = D
4	3	reseq2i 4919	. 2 |- ( B |` C ) = ( B |` D )
5	2, 4	eqtri 2210	1 |- ( A |` C ) = ( B |` D )

Syntax hints:   = wceq 1364   |` cres 4643

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 710  ax-5 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-10 1516  ax-11 1517  ax-i12 1518  ax-bndl 1520  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546  ax-ext 2171

This theorem depends on definitions:  df-bi 117  df-tru 1367  df-nf 1472  df-sb 1774  df-clab 2176  df-cleq 2182  df-clel 2185  df-nfc 2321  df-v 2754  df-in 3150  df-opab 4080  df-xp 4647  df-res 4653

This theorem is referenced by:  cnvresid  5305