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Theorem reseq1i 4930
 Description: Equality inference for restrictions. (Contributed by set.mm contributors, 21-Oct-2014.)
Hypothesis
Ref Expression
reseqi.1 A = B
Assertion
Ref Expression
reseq1i (A C) = (B C)

Proof of Theorem reseq1i
StepHypRef Expression
1 reseqi.1 . 2 A = B
2 reseq1 4928 . 2 (A = B → (A C) = (B C))
31, 2ax-mp 8 1 (A C) = (B C)
 Colors of variables: wff setvar class Syntax hints:   = wceq 1642   ↾ cres 4774 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-v 2861  df-nin 3211  df-compl 3212  df-in 3213  df-res 4788 This theorem is referenced by:  reseq12i  4932  opabresid  5003  coires1  5096  funcnvres2  5167  fcoi1  5240  fvsnun1  5447  fvsnun2  5448  resoprab  5581  resmpt  5696  resmpt2  5697
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