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Theorem ndmaov 46445
Description: The value of an operation outside its domain, analogous to ndmafv 46402. (Contributed by Alexander van der Vekens, 26-May-2017.)
Assertion
Ref Expression
ndmaov (¬ ⟨𝐴, 𝐵⟩ ∈ dom 𝐹 → ((𝐴𝐹𝐵)) = V)

Proof of Theorem ndmaov
StepHypRef Expression
1 df-aov 46383 . 2 ((𝐴𝐹𝐵)) = (𝐹'''⟨𝐴, 𝐵⟩)
2 ndmafv 46402 . 2 (¬ ⟨𝐴, 𝐵⟩ ∈ dom 𝐹 → (𝐹'''⟨𝐴, 𝐵⟩) = V)
31, 2eqtrid 2778 1 (¬ ⟨𝐴, 𝐵⟩ ∈ dom 𝐹 → ((𝐴𝐹𝐵)) = V)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4   = wceq 1533  wcel 2098  Vcvv 3468  cop 4629  dom cdm 5669  '''cafv 46379   ((caov 46380
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-8 2100  ax-9 2108  ax-10 2129  ax-11 2146  ax-12 2163  ax-ext 2697  ax-sep 5292  ax-nul 5299  ax-pr 5420
This theorem depends on definitions:  df-bi 206  df-an 396  df-or 845  df-3an 1086  df-tru 1536  df-fal 1546  df-ex 1774  df-nf 1778  df-sb 2060  df-mo 2528  df-eu 2557  df-clab 2704  df-cleq 2718  df-clel 2804  df-nfc 2879  df-ne 2935  df-ral 3056  df-rex 3065  df-rab 3427  df-v 3470  df-sbc 3773  df-csb 3889  df-dif 3946  df-un 3948  df-in 3950  df-ss 3960  df-nul 4318  df-if 4524  df-sn 4624  df-pr 4626  df-op 4630  df-uni 4903  df-int 4944  df-br 5142  df-opab 5204  df-id 5567  df-xp 5675  df-rel 5676  df-cnv 5677  df-co 5678  df-dm 5679  df-res 5681  df-iota 6488  df-fun 6538  df-fv 6544  df-aiota 46347  df-dfat 46381  df-afv 46382  df-aov 46383
This theorem is referenced by:  ndmaovg  46446  ndmaovcl  46465  ndmaovcom  46467  ndmaovass  46468  ndmaovdistr  46469
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