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Theorem funin 5660
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 3717 . 2
2 funss 5611 . 2
31, 2ax-mp 5 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  i^icin 3474  C_wss 3475  Funwfun 5587
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-v 3111  df-in 3482  df-ss 3489  df-br 4453  df-opab 4511  df-rel 5011  df-cnv 5012  df-co 5013  df-fun 5595
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