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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 31493 | . 2 ⊢ a.e. = {〈𝑎, 𝑚〉 ∣ (𝑚‘(∪ dom 𝑚 ∖ 𝑎)) = 0} | |
2 | 1 | relopabi 5688 | 1 ⊢ Rel a.e. |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1533 ∖ cdif 3932 ∪ cuni 4831 dom cdm 5549 Rel wrel 5554 ‘cfv 6349 0cc0 10531 a.e.cae 31491 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1792 ax-4 1806 ax-5 1907 ax-6 1966 ax-7 2011 ax-8 2112 ax-9 2120 ax-10 2141 ax-11 2157 ax-12 2173 ax-ext 2793 |
This theorem depends on definitions: df-bi 209 df-an 399 df-or 844 df-3an 1085 df-tru 1536 df-ex 1777 df-nf 1781 df-sb 2066 df-clab 2800 df-cleq 2814 df-clel 2893 df-nfc 2963 df-rab 3147 df-v 3496 df-dif 3938 df-un 3940 df-in 3942 df-ss 3951 df-nul 4291 df-if 4467 df-sn 4561 df-pr 4563 df-op 4567 df-opab 5121 df-xp 5555 df-rel 5556 df-ae 31493 |
This theorem is referenced by: (None) |
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