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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
StepHypRef Expression
1 ovexi.1 . 2 𝐴 = (𝐵𝐹𝐶)
2 ovex 6942 . 2 (𝐵𝐹𝐶) ∈ V
31, 2eqeltri 2902 1 𝐴 ∈ V
Colors of variables: wff setvar class
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
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