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Theorem reseq12i 4553
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 (A𝐶) = (B𝐷)

Proof of Theorem reseq12i
StepHypRef Expression
1 reseqi.1 . . 3 A = B
21reseq1i 4551 . 2 (A𝐶) = (B𝐶)
3 reseqi.2 . . 3 𝐶 = 𝐷
43reseq2i 4552 . 2 (B𝐶) = (B𝐷)
52, 4eqtri 2057 1 (A𝐶) = (B𝐷)
Colors of variables: wff set class
Syntax hints:   = wceq 1242  cres 4290
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bndl 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-v 2553  df-in 2918  df-opab 3810  df-xp 4294  df-res 4300
This theorem is referenced by:  cnvresid  4916
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