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Theorem funin 5222
 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 3331 . 2
2 funss 5177 . 2
31, 2ax-mp 10 1
 Colors of variables: wff set class Syntax hints:   wi 6   cin 3093   wss 3094   wfun 4632 This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-7 1535  ax-gen 1536  ax-8 1623  ax-11 1624  ax-17 1628  ax-12o 1664  ax-10 1678  ax-9 1684  ax-4 1692  ax-16 1927  ax-ext 2237 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1315  df-ex 1538  df-nf 1540  df-sb 1884  df-clab 2243  df-cleq 2249  df-clel 2252  df-nfc 2381  df-v 2742  df-in 3101  df-ss 3108  df-br 3964  df-opab 4018  df-rel 4641  df-cnv 4642  df-co 4643  df-fun 4648
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