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Mirrors > Home > MPE Home > Th. List > reldmevls1 | Structured version Visualization version GIF version |
Description: Well-behaved binary operation property of evalSub1. (Contributed by AV, 7-Sep-2019.) |
Ref | Expression |
---|---|
reldmevls1 | ⊢ Rel dom evalSub1 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-evls1 20477 | . 2 ⊢ evalSub1 = (𝑠 ∈ V, 𝑟 ∈ 𝒫 (Base‘𝑠) ↦ ⦋(Base‘𝑠) / 𝑏⦌((𝑥 ∈ (𝑏 ↑m (𝑏 ↑m 1o)) ↦ (𝑥 ∘ (𝑦 ∈ 𝑏 ↦ (1o × {𝑦})))) ∘ ((1o evalSub 𝑠)‘𝑟))) | |
2 | 1 | reldmmpo 7284 | 1 ⊢ Rel dom evalSub1 |
Colors of variables: wff setvar class |
Syntax hints: Vcvv 3494 ⦋csb 3882 𝒫 cpw 4538 {csn 4566 ↦ cmpt 5145 × cxp 5552 dom cdm 5554 ∘ ccom 5558 Rel wrel 5559 ‘cfv 6354 (class class class)co 7155 1oc1o 8094 ↑m cmap 8405 Basecbs 16482 evalSub ces 20283 evalSub1 ces1 20475 |
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 ax-sep 5202 ax-nul 5209 ax-pr 5329 |
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-mo 2618 df-eu 2650 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 4567 df-pr 4569 df-op 4573 df-br 5066 df-opab 5128 df-xp 5560 df-rel 5561 df-dm 5564 df-oprab 7159 df-mpo 7160 df-evls1 20477 |
This theorem is referenced by: evl1fval1 20493 |
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