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Theorem ndmfvg 5236
 Description: The value of a class outside its domain is the empty set. (Contributed by Jim Kingdon, 15-Jan-2019.)
Assertion
Ref Expression
ndmfvg

Proof of Theorem ndmfvg
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 euex 1972 . . . . 5
2 eldmg 4558 . . . . 5
31, 2syl5ibr 154 . . . 4
43con3d 594 . . 3
5 tz6.12-2 5200 . . 3
64, 5syl6 33 . 2
76imp 122 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wa 102   wceq 1285  wex 1422   wcel 1434  weu 1942  cvv 2602  c0 3258   class class class wbr 3793   cdm 4371  cfv 4932 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in1 577  ax-in2 578  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2064 This theorem depends on definitions:  df-bi 115  df-3an 922  df-tru 1288  df-fal 1291  df-nf 1391  df-sb 1687  df-eu 1945  df-clab 2069  df-cleq 2075  df-clel 2078  df-nfc 2209  df-ral 2354  df-rex 2355  df-v 2604  df-dif 2976  df-un 2978  df-in 2980  df-ss 2987  df-nul 3259  df-sn 3412  df-pr 3413  df-op 3415  df-uni 3610  df-br 3794  df-dm 4381  df-iota 4897  df-fv 4940 This theorem is referenced by:  ovprc  5571
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