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Theorem funres 5143
 Description: A restriction of a function is a function. Compare Exercise 18 of [TakeutiZaring] p. 25. (Contributed by set.mm contributors, 16-Aug-1994.)
Assertion
Ref Expression
funres

Proof of Theorem funres
StepHypRef Expression
1 resss 4988 . 2
2 funss 5126 . 2
31, 2ax-mp 5 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wss 3257   cres 4774   wfun 4775 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 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-ss 3259  df-opab 4623  df-br 4640  df-co 4726  df-cnv 4785  df-res 4788  df-fun 4789 This theorem is referenced by:  fnssresb  5195  fnresi  5200  fores  5278  respreima  5410  funfvima  5459
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