Theorem reseq12i 5980

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 5978	. 2 ⊢ (𝐴 ↾ 𝐶) = (𝐵 ↾ 𝐶)
3		reseqi.2	. . 3 ⊢ 𝐶 = 𝐷
4	3	reseq2i 5979	. 2 ⊢ (𝐵 ↾ 𝐶) = (𝐵 ↾ 𝐷)
5	2, 4	eqtri 2786	1 ⊢ (𝐴 ↾ 𝐶) = (𝐵 ↾ 𝐷)

This proof depends on syntax axioms:   = wceq 1570   ↾ cres 5658

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 1945  ax-6 2002  ax-7 2043  ax-8 2149  ax-9 2157  ax-ext 2735

This proof depends on definitions:  df-bi 210  df-an 402  df-tru 1573  df-ex 1813  df-sb 2102  df-clab 2742  df-cleq 2755  df-clel 2839  df-rab 3417  df-in 4094  df-opab 5172  df-xp 5662  df-res 5668

This theorem is used by:  cnvresidOLD  6644  fprlem1  8349  dfoi  9535  frrlem15  9791  lubfval  18554  glbfval  18567  odulub  18611  oduglb  18613  dvlog  27012  dvlog2  27014  issubgr  29885  finsumvtxdg2size  30164  sitgclg  35057  fourierdlem57  47388  fourierdlem74  47405  fourierdlem75  47406