Theorem reseq12i 4610

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 4608	. 2 |- ( A |` C ) = ( B |` C )
3		reseqi.2	. . 3 |- C = D
4	3	reseq2i 4609	. 2 |- ( B |` C ) = ( B |` D )
5	2, 4	eqtri 2060	1 |- ( A |` C ) = ( B |` D )

Syntax hints:   = wceq 1243   |` cres 4347

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022

This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-v 2559  df-in 2924  df-opab 3819  df-xp 4351  df-res 4357

This theorem is referenced by:  cnvresid  4973