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Theorem reldmevls1 17870
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 17868 . 2  |- evalSub1  =  ( s  e.  _V ,  r  e. 
~P ( Base `  s
)  |->  [_ ( Base `  s
)  /  b ]_ ( ( x  e.  ( b  ^m  (
b  ^m  1o )
)  |->  ( x  o.  ( y  e.  b 
|->  ( 1o  X.  {
y } ) ) ) )  o.  (
( 1o evalSub  s ) `  r ) ) )
21reldmmpt2 6304 1  |-  Rel  dom evalSub1
Colors of variables: wff setvar class
Syntax hints:   _Vcvv 3071   [_csb 3389   ~Pcpw 3961   {csn 3978    |-> cmpt 4451    X. cxp 4939   dom cdm 4941    o. ccom 4945   Rel wrel 4946   ` cfv 5519  (class class class)co 6193   1oc1o 7016    ^m cmap 7317   Basecbs 14285   evalSub ces 17702   evalSub1 ces1 17866
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-5 1671  ax-6 1710  ax-7 1730  ax-9 1762  ax-10 1777  ax-11 1782  ax-12 1794  ax-13 1952  ax-ext 2430  ax-sep 4514  ax-nul 4522  ax-pr 4632
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 967  df-tru 1373  df-ex 1588  df-nf 1591  df-sb 1703  df-eu 2264  df-mo 2265  df-clab 2437  df-cleq 2443  df-clel 2446  df-nfc 2601  df-ne 2646  df-ral 2800  df-rex 2801  df-rab 2804  df-v 3073  df-dif 3432  df-un 3434  df-in 3436  df-ss 3443  df-nul 3739  df-if 3893  df-sn 3979  df-pr 3981  df-op 3985  df-br 4394  df-opab 4452  df-xp 4947  df-rel 4948  df-dm 4951  df-oprab 6197  df-mpt2 6198  df-evls1 17868
This theorem is referenced by:  evl1fval1  17883
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