| Mathbox for Thierry Arnoux |
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| Mirrors > Home > MPE Home > Th. List > Mathboxes > relae | Structured version Visualization version GIF version | ||
| Description: 'almost everywhere' is a relation. (Contributed by Thierry Arnoux, 20-Oct-2017.) |
| Ref | Expression |
|---|---|
| relae | ⊢ Rel a.e. |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | df-ae 34218 | . 2 ⊢ a.e. = {〈𝑎, 𝑚〉 ∣ (𝑚‘(∪ dom 𝑚 ∖ 𝑎)) = 0} | |
| 2 | 1 | relopabiv 5828 | 1 ⊢ Rel a.e. |
| Colors of variables: wff setvar class |
| Syntax hints: = wceq 1540 ∖ cdif 3947 ∪ cuni 4905 dom cdm 5683 Rel wrel 5688 ‘cfv 6559 0cc0 11151 a.e.cae 34216 |
| This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1795 ax-4 1809 ax-5 1910 ax-6 1967 ax-7 2007 ax-8 2110 ax-9 2118 ax-ext 2707 |
| This theorem depends on definitions: df-bi 207 df-an 396 df-tru 1543 df-ex 1780 df-sb 2065 df-clab 2714 df-cleq 2728 df-clel 2815 df-v 3481 df-ss 3967 df-opab 5204 df-xp 5689 df-rel 5690 df-ae 34218 |
| This theorem is referenced by: (None) |
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