Theorem reseq12i 5981

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 5979	. 2 ⊢ (𝐴 ↾ 𝐶) = (𝐵 ↾ 𝐶)
3		reseqi.2	. . 3 ⊢ 𝐶 = 𝐷
4	3	reseq2i 5980	. 2 ⊢ (𝐵 ↾ 𝐶) = (𝐵 ↾ 𝐷)
5	2, 4	eqtri 2789	1 ⊢ (𝐴 ↾ 𝐶) = (𝐵 ↾ 𝐷)

This proof depends on syntax axioms:   = wceq 1570   ↾ cres 5668

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842  ax-5 1943  ax-6 2000  ax-7 2041  ax-8 2148  ax-9 2156  ax-ext 2738

This proof depends on definitions:  df-bi 210  df-an 402  df-tru 1573  df-ex 1813  df-sb 2100  df-clab 2745  df-cleq 2758  df-clel 2841  df-rab 3420  df-in 3915  df-opab 5179  df-xp 5672  df-res 5678

This theorem is used by:  cnvresid  6622  fprlem1  8306  dfoi  9483  frrlem15  9739  lubfval  18429  glbfval  18442  odulub  18486  oduglb  18488  dvlog  26853  dvlog2  26855  issubgr  29658  finsumvtxdg2size  29937  sitgclg  34764  fourierdlem57  46918  fourierdlem74  46935  fourierdlem75  46936