Theorem resex 4932

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 4931	. 2 |- ( A e. _V -> ( A |` B ) e. _V )
3	1, 2	ax-mp 5	1 |- ( A |` B ) e. _V

Syntax hints:   e. wcel 2141   _Vcvv 2730   |` cres 4613

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 704  ax-5 1440  ax-7 1441  ax-gen 1442  ax-ie1 1486  ax-ie2 1487  ax-8 1497  ax-10 1498  ax-11 1499  ax-i12 1500  ax-bndl 1502  ax-4 1503  ax-17 1519  ax-i9 1523  ax-ial 1527  ax-i5r 1528  ax-ext 2152  ax-sep 4107

This theorem depends on definitions:  df-bi 116  df-tru 1351  df-nf 1454  df-sb 1756  df-clab 2157  df-cleq 2163  df-clel 2166  df-nfc 2301  df-v 2732  df-in 3127  df-ss 3134  df-res 4623

This theorem is referenced by:  sbthlemi10  6943  finomni  7116  ctinf  12385