Theorem fvexi 6202

Description: The value of a class exists. Inference form of fvex 6201. (Contributed by Glauco Siliprandi, 23-Oct-2021.)

Hypothesis

Ref	Expression
fvexi.1	|- A = ( F ` B )

Assertion

Ref	Expression
fvexi	|- A e. _V

Proof of Theorem fvexi

Step	Hyp	Ref	Expression
1		fvexi.1	. 2 |- A = ( F ` B )
2		fvex 6201	. 2 |- ( F ` B ) e. _V
3	1, 2	eqeltri 2697	1 |- A e. _V

Syntax hints:   = wceq 1483   e. wcel 1990   _Vcvv 3200   ` cfv 5888

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-9 1999  ax-10 2019  ax-11 2034  ax-12 2047  ax-13 2246  ax-ext 2602  ax-nul 4789

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1486  df-ex 1705  df-nf 1710  df-sb 1881  df-eu 2474  df-clab 2609  df-cleq 2615  df-clel 2618  df-nfc 2753  df-ral 2917  df-rex 2918  df-v 3202  df-sbc 3436  df-dif 3577  df-un 3579  df-in 3581  df-ss 3588  df-nul 3916  df-sn 4178  df-pr 4180  df-uni 4437  df-iota 5851  df-fv 5896

This theorem is referenced by:  rmodislmod  18931  setsvtx  25927  usgredgffibi  26216  vtxdginducedm1lem1  26435  vtxdginducedm1lem4  26438  vtxdginducedm1  26439  vtxdginducedm1fi  26440  finsumvtxdg2ssteplem4  26444  frgrwopreg1  27182  eulerpartlemgvv  30438  limsupequzmpt2  39950  climuzlem  39975  climisp  39978  climxrrelem  39981  climxrre  39982  limsupgtlem  40009  liminflelimsupuz  40017  liminfgelimsupuz  40020  liminfequzmpt2  40023  liminfvaluz  40024  limsupvaluz3  40030  climliminflimsupd  40033  liminfreuzlem  40034  liminfltlem  40036  liminflimsupclim  40039  xlimclim2lem  40065  climxlim2  40072  smflimmpt  41016  smflimsuplem4  41029  smflimsuplem6  41031  smflimsuplem8  41033  smfliminflem  41036  isupwlkg  41718