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Theorem ndmfvg 5452
 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 2029 . . . . 5
2 eldmg 4734 . . . . 5
31, 2syl5ibr 155 . . . 4
43con3d 620 . . 3
5 tz6.12-2 5412 . . 3
64, 5syl6 33 . 2
76imp 123 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wa 103   wceq 1331  wex 1468   wcel 1480  weu 1999  cvv 2686  c0 3363   class class class wbr 3929   cdm 4539  cfv 5123 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 603  ax-in2 604  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121 This theorem depends on definitions:  df-bi 116  df-3an 964  df-tru 1334  df-fal 1337  df-nf 1437  df-sb 1736  df-eu 2002  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-ral 2421  df-rex 2422  df-v 2688  df-dif 3073  df-un 3075  df-in 3077  df-ss 3084  df-nul 3364  df-sn 3533  df-pr 3534  df-op 3536  df-uni 3737  df-br 3930  df-dm 4549  df-iota 5088  df-fv 5131 This theorem is referenced by:  ovprc  5806  sumnul  11200
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