Theorem resex 4960

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 4959	. 2 |- ( A e. _V -> ( A |` B ) e. _V )
3	1, 2	ax-mp 5	1 |- ( A |` B ) e. _V

Syntax hints:   e. wcel 2158   _Vcvv 2749   |` cres 4640

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 710  ax-5 1457  ax-7 1458  ax-gen 1459  ax-ie1 1503  ax-ie2 1504  ax-8 1514  ax-10 1515  ax-11 1516  ax-i12 1517  ax-bndl 1519  ax-4 1520  ax-17 1536  ax-i9 1540  ax-ial 1544  ax-i5r 1545  ax-ext 2169  ax-sep 4133

This theorem depends on definitions:  df-bi 117  df-tru 1366  df-nf 1471  df-sb 1773  df-clab 2174  df-cleq 2180  df-clel 2183  df-nfc 2318  df-v 2751  df-in 3147  df-ss 3154  df-res 4650

This theorem is referenced by:  sbthlemi10  6979  finomni  7152  ctinf  12445