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Theorem aovnfundmuv 41583
Description: If an ordered pair is not in the domain of a class or the class is not a function restricted to the ordered pair, then the operation value for this pair is the universal class. (Contributed by Alexander van der Vekens, 26-May-2017.)
Assertion
Ref Expression
aovnfundmuv 𝐹 defAt ⟨𝐴, 𝐵⟩ → ((𝐴𝐹𝐵)) = V)

Proof of Theorem aovnfundmuv
StepHypRef Expression
1 df-aov 41519 . 2 ((𝐴𝐹𝐵)) = (𝐹'''⟨𝐴, 𝐵⟩)
2 afvnfundmuv 41540 . 2 𝐹 defAt ⟨𝐴, 𝐵⟩ → (𝐹'''⟨𝐴, 𝐵⟩) = V)
31, 2syl5eq 2697 1 𝐹 defAt ⟨𝐴, 𝐵⟩ → ((𝐴𝐹𝐵)) = V)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4   = wceq 1523  Vcvv 3231  cop 4216   defAt wdfat 41514  '''cafv 41515   ((caov 41516
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1762  ax-4 1777  ax-5 1879  ax-6 1945  ax-7 1981  ax-9 2039  ax-10 2059  ax-11 2074  ax-12 2087  ax-13 2282  ax-ext 2631
This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-tru 1526  df-ex 1745  df-nf 1750  df-sb 1938  df-clab 2638  df-cleq 2644  df-clel 2647  df-nfc 2782  df-rab 2950  df-v 3233  df-un 3612  df-if 4120  df-fv 5934  df-afv 41518  df-aov 41519
This theorem is referenced by: (None)
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