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Theorem ndmfvg 5147
Description: The value of a class outside its domain is the empty set. (Contributed by Jim Kingdon, 15-Jan-2019.)
Assertion
Ref Expression
ndmfvg  _V  dom  F  F `  (/)

Proof of Theorem ndmfvg
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 euex 1927 . . . . 5  F  F
2 eldmg 4473 . . . . 5  _V  dom  F  F
31, 2syl5ibr 145 . . . 4  _V  F  dom  F
43con3d 560 . . 3  _V  dom  F  F
5 tz6.12-2 5112 . . 3  F  F `  (/)
64, 5syl6 29 . 2  _V  dom  F  F `  (/)
76imp 115 1  _V  dom  F  F `  (/)
Colors of variables: wff set class
Syntax hints:   wn 3   wi 4   wa 97   wceq 1242  wex 1378   wcel 1390  weu 1897   _Vcvv 2551   (/)c0 3218   class class class wbr 3755   dom cdm 4288   ` cfv 4845
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bndl 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-3an 886  df-tru 1245  df-fal 1248  df-nf 1347  df-sb 1643  df-eu 1900  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-ral 2305  df-rex 2306  df-v 2553  df-dif 2914  df-un 2916  df-in 2918  df-ss 2925  df-nul 3219  df-sn 3373  df-pr 3374  df-op 3376  df-uni 3572  df-br 3756  df-dm 4298  df-iota 4810  df-fv 4853
This theorem is referenced by:  ovprc  5482
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