Theorem resex 4855

Description: The restriction of a set is a set. (Contributed by Jeff Madsen, 19-Jun-2011.)

Hypothesis

Ref	Expression
resex.1	|- A e. _V

Assertion

Ref	Expression
resex	|- ( A |` B ) e. _V

Proof of Theorem resex

Step	Hyp	Ref	Expression
1		resex.1	. 2 |- A e. _V
2		resexg 4854	. 2 |- ( A e. _V -> ( A |` B ) e. _V )
3	1, 2	ax-mp 5	1 |- ( A |` B ) e. _V

Syntax hints:   e. wcel 1480   _Vcvv 2681   |` cres 4536

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2119  ax-sep 4041

This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2124  df-cleq 2130  df-clel 2133  df-nfc 2268  df-v 2683  df-in 3072  df-ss 3079  df-res 4546

This theorem is referenced by:  sbthlemi10  6847  finomni  7005  ctinf  11932