Theorem reseq12i 4976

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 4974	. 2 |- ( A |` C ) = ( B |` C )
3		reseqi.2	. . 3 |- C = D
4	3	reseq2i 4975	. 2 |- ( B |` C ) = ( B |` D )
5	2, 4	eqtri 2228	1 |- ( A |` C ) = ( B |` D )

Syntax hints:   = wceq 1373   |` cres 4695

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 1471  ax-7 1472  ax-gen 1473  ax-ie1 1517  ax-ie2 1518  ax-8 1528  ax-10 1529  ax-11 1530  ax-i12 1531  ax-bndl 1533  ax-4 1534  ax-17 1550  ax-i9 1554  ax-ial 1558  ax-i5r 1559  ax-ext 2189

This theorem depends on definitions:  df-bi 117  df-tru 1376  df-nf 1485  df-sb 1787  df-clab 2194  df-cleq 2200  df-clel 2203  df-nfc 2339  df-v 2778  df-in 3180  df-opab 4122  df-xp 4699  df-res 4705

This theorem is referenced by:  cnvresid  5367