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Theorem ovexi 6633
 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 6632 . 2 (𝐵𝐹𝐶) ∈ V
31, 2eqeltri 2694 1 𝐴 ∈ V
 Colors of variables: wff setvar class Syntax hints:   = wceq 1480   ∈ wcel 1987  Vcvv 3186  (class class class)co 6604 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1719  ax-4 1734  ax-5 1836  ax-6 1885  ax-7 1932  ax-9 1996  ax-10 2016  ax-11 2031  ax-12 2044  ax-13 2245  ax-ext 2601  ax-nul 4749 This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1483  df-ex 1702  df-nf 1707  df-sb 1878  df-eu 2473  df-clab 2608  df-cleq 2614  df-clel 2617  df-nfc 2750  df-ral 2912  df-rex 2913  df-v 3188  df-sbc 3418  df-dif 3558  df-un 3560  df-in 3562  df-ss 3569  df-nul 3892  df-sn 4149  df-pr 4151  df-uni 4403  df-iota 5810  df-fv 5855  df-ov 6607 This theorem is referenced by:  negex  10223  decex  11442  nghmfval  22436  konigsberglem5  26984  cdleme31snd  35151  subsalsal  39881  dpval  41801
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