Theorem fvex 5339

Description: The value of a class exists. Corollary 6.13 of [TakeutiZaring] p. 27. (Contributed by set.mm contributors, 30-Dec-1996.)

Assertion

Ref	Expression
fvex	|- (F` A) e. _V

Proof of Theorem fvex

Dummy variable x is distinct from all other variables.

Step	Hyp	Ref	Expression
1		df-fv 4795	. 2 |- (F` A) = (iotaxAFx)
2		iotaex 4356	. 2 |- (iotaxAFx) e. _V
3	1, 2	eqeltri 2423	1 |- (F` A) e. _V

Syntax hints:   e. wcel 1710  _Vcvv 2859  iotacio 4337   class class class wbr 4639  ` cfv 4781

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 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 4078

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 2478  df-ne 2518  df-ral 2619  df-rex 2620  df-v 2861  df-sbc 3047  df-nin 3211  df-compl 3212  df-in 3213  df-un 3214  df-dif 3215  df-ss 3259  df-nul 3551  df-sn 3741  df-pr 3742  df-uni 3892  df-iota 4339  df-fv 4795

This theorem is referenced by:  dffn5  5363  fvelrnb  5365  funimass4  5368  fvelimab  5370  fniinfv  5372  funfv  5375  dmfco  5381  fvimacnvi  5402  fvimacnv  5403  funconstss  5406  fsn2  5434  fnressn  5438  fniunfv  5466  funiunfv  5467  dff13  5471  isomin  5496  f1oiso  5499  ovex  5551  fvmptex  5721  fvmptnf  5723  txpcofun  5803  enprmaplem3  6078  nenpw1pwlem1  6084  1cnc  6139  nchoicelem6  6292  nchoicelem7  6293  nchoicelem12  6298  nchoicelem13  6299  nchoicelem14  6300  nchoicelem17  6303