Theorem reseq12i 5964

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 5962	. 2 ⊢ (𝐴 ↾ 𝐶) = (𝐵 ↾ 𝐶)
3		reseqi.2	. . 3 ⊢ 𝐶 = 𝐷
4	3	reseq2i 5963	. 2 ⊢ (𝐵 ↾ 𝐶) = (𝐵 ↾ 𝐷)
5	2, 4	eqtri 2758	1 ⊢ (𝐴 ↾ 𝐶) = (𝐵 ↾ 𝐷)

Syntax hints:   = wceq 1540   ↾ cres 5656

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-ext 2707

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1543  df-ex 1780  df-sb 2065  df-clab 2714  df-cleq 2727  df-clel 2809  df-rab 3416  df-in 3933  df-opab 5182  df-xp 5660  df-res 5666

This theorem is referenced by:  cnvresid  6615  fprlem1  8299  wfrlem5OLD  8327  dfoi  9525  frrlem15  9771  lubfval  18360  glbfval  18373  odulub  18417  oduglb  18419  dvlog  26612  dvlog2  26614  issubgr  29250  finsumvtxdg2size  29530  sitgclg  34374  fourierdlem57  46192  fourierdlem74  46209  fourierdlem75  46210