Theorem ovex 5552

Description: The result of an operation is a set. (Contributed by set.mm contributors, 13-Mar-1995.)

Assertion

Ref	Expression
ovex	|- (AFB) e. _V

Proof of Theorem ovex

Step	Hyp	Ref	Expression
1		df-ov 5527	. 2 |- (AFB) = (F` <.A, B>.)
2		fvex 5340	. 2 |- (F` <.A, B>.) e. _V
3	1, 2	eqeltri 2423	1 |- (AFB) e. _V

Syntax hints:   e. wcel 1710  _Vcvv 2860  <.cop 4562  ` cfv 4782  (class class class)co 5526

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  ax-nin 4079

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-eu 2208  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2479  df-ne 2519  df-ral 2620  df-rex 2621  df-v 2862  df-sbc 3048  df-nin 3212  df-compl 3213  df-in 3214  df-un 3215  df-dif 3216  df-ss 3260  df-nul 3552  df-sn 3742  df-pr 3743  df-uni 3893  df-iota 4340  df-fv 4796  df-ov 5527

This theorem is referenced by:  ovelrn  5609  ndmovass  5619  ndmovdistr  5620  caov4  5640  caov411  5641  caovdir  5643  caovdilem  5644  caovlem2  5645  enmap2lem1  6064  enmap1lem1  6070  enprmaplem1  6077  ovcelem1  6172  ceex  6175  ce0nnul  6178  ce0nnulb  6183  ceclb  6184  fce  6189  ce0  6191  ce2  6193  ncvsq  6257  spaccl  6287  spacind  6288  spacis  6289  nchoicelem9  6298