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Mirrors > Home > MPE Home > Th. List > Mathboxes > aovnfundmuv | Structured version Visualization version GIF version |
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.) |
Ref | Expression |
---|---|
aovnfundmuv | ⊢ (¬ 𝐹 defAt 〈𝐴, 𝐵〉 → ((𝐴𝐹𝐵)) = V) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-aov 41198 | . 2 ⊢ ((𝐴𝐹𝐵)) = (𝐹'''〈𝐴, 𝐵〉) | |
2 | afvnfundmuv 41219 | . 2 ⊢ (¬ 𝐹 defAt 〈𝐴, 𝐵〉 → (𝐹'''〈𝐴, 𝐵〉) = V) | |
3 | 1, 2 | syl5eq 2668 | 1 ⊢ (¬ 𝐹 defAt 〈𝐴, 𝐵〉 → ((𝐴𝐹𝐵)) = V) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 → wi 4 = wceq 1483 Vcvv 3200 〈cop 4183 defAt wdfat 41193 '''cafv 41194 ((caov 41195 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-rab 2921 df-v 3202 df-un 3579 df-if 4087 df-fv 5896 df-afv 41197 df-aov 41198 |
This theorem is referenced by: (None) |
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