Theorem ovexi 6943

Description: The result of an operation is a set. (Contributed by Glauco Siliprandi, 26-Jun-2021.)

Hypothesis

Ref	Expression
ovexi.1	⊢ 𝐴 = (𝐵𝐹𝐶)

Assertion

Ref	Expression
ovexi	⊢ 𝐴 ∈ V

Proof of Theorem ovexi

Step	Hyp	Ref	Expression
1		ovexi.1	. 2 ⊢ 𝐴 = (𝐵𝐹𝐶)
2		ovex 6942	. 2 ⊢ (𝐵𝐹𝐶) ∈ V
3	1, 2	eqeltri 2902	1 ⊢ 𝐴 ∈ V

Syntax hints:   = wceq 1656   ∈ wcel 2164  Vcvv 3414  (class class class)co 6910

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1894  ax-4 1908  ax-5 2009  ax-6 2075  ax-7 2112  ax-9 2173  ax-10 2192  ax-11 2207  ax-12 2220  ax-13 2389  ax-ext 2803  ax-nul 5015

This theorem depends on definitions:  df-bi 199  df-an 387  df-or 879  df-tru 1660  df-ex 1879  df-nf 1883  df-sb 2068  df-mo 2605  df-eu 2640  df-clab 2812  df-cleq 2818  df-clel 2821  df-nfc 2958  df-ral 3122  df-rex 3123  df-v 3416  df-sbc 3663  df-dif 3801  df-un 3803  df-in 3805  df-ss 3812  df-nul 4147  df-sn 4400  df-pr 4402  df-uni 4661  df-iota 6090  df-fv 6135  df-ov 6913

This theorem is referenced by:  negex  10606  decex  11832  gsumress  17636  nghmfval  22903  2pthon3v  27279  konigsberglem5  27631  dpval  30139  cdleme31snd  36456  c0exALT  38044  subsalsal  41362  rrxline  43298