Theorem reseq12i 5011

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 5009	. 2 |- ( A |` C ) = ( B |` C )
3		reseqi.2	. . 3 |- C = D
4	3	reseq2i 5010	. 2 |- ( B |` C ) = ( B |` D )
5	2, 4	eqtri 2252	1 |- ( A |` C ) = ( B |` D )

Syntax hints:   = wceq 1397   |` cres 4727

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 716  ax-5 1495  ax-7 1496  ax-gen 1497  ax-ie1 1541  ax-ie2 1542  ax-8 1552  ax-10 1553  ax-11 1554  ax-i12 1555  ax-bndl 1557  ax-4 1558  ax-17 1574  ax-i9 1578  ax-ial 1582  ax-i5r 1583  ax-ext 2213

This theorem depends on definitions:  df-bi 117  df-tru 1400  df-nf 1509  df-sb 1811  df-clab 2218  df-cleq 2224  df-clel 2227  df-nfc 2363  df-v 2804  df-in 3206  df-opab 4151  df-xp 4731  df-res 4737

This theorem is referenced by:  cnvresid  5404  issubgr  16107