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Theorem fssresd 5255
 Description: Restriction of a function with a subclass of its domain, deduction form. (Contributed by Glauco Siliprandi, 11-Dec-2019.)
Hypotheses
Ref Expression
fssresd.1
fssresd.2
Assertion
Ref Expression
fssresd

Proof of Theorem fssresd
StepHypRef Expression
1 fssresd.1 . 2
2 fssresd.2 . 2
3 fssres 5254 . 2
41, 2, 3syl2anc 406 1
 Colors of variables: wff set class Syntax hints:   wi 4   wss 3035   cres 4499  wf 5075 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 681  ax-5 1404  ax-7 1405  ax-gen 1406  ax-ie1 1450  ax-ie2 1451  ax-8 1463  ax-10 1464  ax-11 1465  ax-i12 1466  ax-bndl 1467  ax-4 1468  ax-14 1473  ax-17 1487  ax-i9 1491  ax-ial 1495  ax-i5r 1496  ax-ext 2095  ax-sep 4004  ax-pow 4056  ax-pr 4089 This theorem depends on definitions:  df-bi 116  df-3an 945  df-tru 1315  df-nf 1418  df-sb 1717  df-clab 2100  df-cleq 2106  df-clel 2109  df-nfc 2242  df-ral 2393  df-rex 2394  df-v 2657  df-un 3039  df-in 3041  df-ss 3048  df-pw 3476  df-sn 3497  df-pr 3498  df-op 3500  df-br 3894  df-opab 3948  df-xp 4503  df-rel 4504  df-cnv 4505  df-co 4506  df-dm 4507  df-rn 4508  df-res 4509  df-fun 5081  df-fn 5082  df-f 5083 This theorem is referenced by:  cnrest  12240  cnptopresti  12243  cnptoprest  12244  psmetres2  12316  xmetres2  12362  metres2  12364  xmetresbl  12423  rescncf  12548  trilpolemlt1  12915
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