Theorem reseq12i 5951

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 5949	. 2 ⊢ (𝐴 ↾ 𝐶) = (𝐵 ↾ 𝐶)
3		reseqi.2	. . 3 ⊢ 𝐶 = 𝐷
4	3	reseq2i 5950	. 2 ⊢ (𝐵 ↾ 𝐶) = (𝐵 ↾ 𝐷)
5	2, 4	eqtri 2753	1 ⊢ (𝐴 ↾ 𝐶) = (𝐵 ↾ 𝐷)

Syntax hints:   = wceq 1540   ↾ cres 5643

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 2008  ax-8 2111  ax-9 2119  ax-ext 2702

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1543  df-ex 1780  df-sb 2066  df-clab 2709  df-cleq 2722  df-clel 2804  df-rab 3409  df-in 3924  df-opab 5173  df-xp 5647  df-res 5653

This theorem is referenced by:  cnvresid  6598  fprlem1  8282  dfoi  9471  frrlem15  9717  lubfval  18316  glbfval  18329  odulub  18373  oduglb  18375  dvlog  26567  dvlog2  26569  issubgr  29205  finsumvtxdg2size  29485  sitgclg  34340  fourierdlem57  46168  fourierdlem74  46185  fourierdlem75  46186