Theorem reseq12i 5936

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 5934	. 2 ⊢ (𝐴 ↾ 𝐶) = (𝐵 ↾ 𝐶)
3		reseqi.2	. . 3 ⊢ 𝐶 = 𝐷
4	3	reseq2i 5935	. 2 ⊢ (𝐵 ↾ 𝐶) = (𝐵 ↾ 𝐷)
5	2, 4	eqtri 2760	1 ⊢ (𝐴 ↾ 𝐶) = (𝐵 ↾ 𝐷)

Syntax hints:   = wceq 1542   ↾ cres 5626

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1969  ax-7 2010  ax-8 2116  ax-9 2124  ax-ext 2709

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1545  df-ex 1782  df-sb 2069  df-clab 2716  df-cleq 2729  df-clel 2812  df-rab 3391  df-in 3897  df-opab 5149  df-xp 5630  df-res 5636

This theorem is referenced by:  cnvresid  6571  fprlem1  8243  dfoi  9419  frrlem15  9672  lubfval  18305  glbfval  18318  odulub  18362  oduglb  18364  dvlog  26628  dvlog2  26630  issubgr  29354  finsumvtxdg2size  29634  sitgclg  34502  fourierdlem57  46609  fourierdlem74  46626  fourierdlem75  46627