Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  funin Structured version   Unicode version

Theorem funin 5512
 Description: The intersection with a function is a function. Exercise 14(a) of [Enderton] p. 53. (Contributed by NM, 19-Mar-2004.) (Proof shortened by Andrew Salmon, 17-Sep-2011.)
Assertion
Ref Expression
funin

Proof of Theorem funin
StepHypRef Expression
1 inss1 3553 . 2
2 funss 5464 . 2
31, 2ax-mp 8 1
 Colors of variables: wff set class Syntax hints:   wi 4   cin 3311   wss 3312   wfun 5440 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-v 2950  df-in 3319  df-ss 3326  df-br 4205  df-opab 4259  df-rel 4877  df-cnv 4878  df-co 4879  df-fun 5448
 Copyright terms: Public domain W3C validator