Theorem reseq12i 5987

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 5985	. 2 ⊢ (𝐴 ↾ 𝐶) = (𝐵 ↾ 𝐶)
3		reseqi.2	. . 3 ⊢ 𝐶 = 𝐷
4	3	reseq2i 5986	. 2 ⊢ (𝐵 ↾ 𝐶) = (𝐵 ↾ 𝐷)
5	2, 4	eqtri 2756	1 ⊢ (𝐴 ↾ 𝐶) = (𝐵 ↾ 𝐷)

Syntax hints:   = wceq 1533   ↾ cres 5684

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-8 2100  ax-9 2108  ax-ext 2699

This theorem depends on definitions:  df-bi 206  df-an 395  df-tru 1536  df-ex 1774  df-sb 2060  df-clab 2706  df-cleq 2720  df-clel 2806  df-rab 3431  df-in 3956  df-opab 5215  df-xp 5688  df-res 5694

This theorem is referenced by:  cnvresid  6637  fprlem1  8312  wfrlem5OLD  8340  dfoi  9542  frrlem15  9788  lubfval  18349  glbfval  18362  odulub  18406  oduglb  18408  dvlog  26605  dvlog2  26607  issubgr  29104  finsumvtxdg2size  29384  sitgclg  33995  fourierdlem57  45580  fourierdlem74  45597  fourierdlem75  45598