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Theorem funin 5163
Description: The intersection with a function is a function. Exercise 14(a) of [Enderton] p. 53. (The proof was shortened by Andrew Salmon, 17-Sep-2011.) (Contributed by set.mm contributors, 19-Mar-2004.) (Revised by set.mm contributors, 18-Sep-2011.)
Assertion
Ref Expression
funin

Proof of Theorem funin
StepHypRef Expression
1 inss1 3475 . 2
2 funss 5126 . 2
31, 2ax-mp 5 1
Colors of variables: wff setvar class
Syntax hints:   wi 4   cin 3208   wss 3257   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-fun 4789
This theorem is referenced by: (None)
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