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Theorem reldmevls1 22245
Description: Well-behaved binary operation property of evalSub1. (Contributed by AV, 7-Sep-2019.)
Assertion
Ref Expression
reldmevls1 Rel dom evalSub1

Proof of Theorem reldmevls1
Dummy variables 𝑟 𝑏 𝑠 𝑥 𝑦 are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 df-evls1 22243 . 2 evalSub1 = (𝑠 ∈ V, 𝑟 ∈ 𝒫 (Base‘𝑠) ↦ (Base‘𝑠) / 𝑏((𝑥 ∈ (𝑏m (𝑏m 1o)) ↦ (𝑥 ∘ (𝑦𝑏 ↦ (1o × {𝑦})))) ∘ ((1o evalSub 𝑠)‘𝑟)))
21reldmmpo 7552 1 Rel dom evalSub1
Colors of variables: wff setvar class
Syntax hints:  Vcvv 3463  csb 3884  𝒫 cpw 4598  {csn 4624  cmpt 5226   × cxp 5670  dom cdm 5672  ccom 5676  Rel wrel 5677  cfv 6543  (class class class)co 7416  1oc1o 8478  m cmap 8843  Basecbs 17179   evalSub ces 22023   evalSub1 ces1 22241
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 2166  ax-ext 2696  ax-sep 5294  ax-nul 5301  ax-pr 5423
This theorem depends on definitions:  df-bi 206  df-an 395  df-or 846  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 2703  df-cleq 2717  df-clel 2802  df-nfc 2877  df-rab 3420  df-v 3465  df-dif 3942  df-un 3944  df-ss 3956  df-nul 4319  df-if 4525  df-sn 4625  df-pr 4627  df-op 4631  df-br 5144  df-opab 5206  df-xp 5678  df-rel 5679  df-dm 5682  df-oprab 7420  df-mpo 7421  df-evls1 22243
This theorem is referenced by:  evl1fval1  22259
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