Theorem reseq12i 5394

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 5392	. 2 |- ( A |` C ) = ( B |` C )
3		reseqi.2	. . 3 |- C = D
4	3	reseq2i 5393	. 2 |- ( B |` C ) = ( B |` D )
5	2, 4	eqtri 2644	1 |- ( A |` C ) = ( B |` D )

Syntax hints:   = wceq 1483   |` cres 5116

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-9 1999  ax-10 2019  ax-11 2034  ax-12 2047  ax-13 2246  ax-ext 2602

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1486  df-ex 1705  df-nf 1710  df-sb 1881  df-clab 2609  df-cleq 2615  df-clel 2618  df-nfc 2753  df-v 3202  df-in 3581  df-opab 4713  df-xp 5120  df-res 5126

This theorem is referenced by:  cnvresid  5968  wfrlem5  7419  dfoi  8416  lubfval  16978  glbfval  16991  oduglb  17139  odulub  17141  dvlog  24397  dvlog2  24399  issubgr  26163  finsumvtxdg2size  26446  sitgclg  30404  frrlem5  31784  fourierdlem57  40380  fourierdlem74  40397  fourierdlem75  40398