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Theorem supp0prc 6921
 Description: The support of a class is empty if either the class or the "zero" is a proper class. . (Contributed by AV, 28-May-2019.)
Assertion
Ref Expression
supp0prc

Proof of Theorem supp0prc
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 df-supp 6919 . 2
21mpt2ndm0 6516 1
 Colors of variables: wff setvar class Syntax hints:  -.wn 3  ->wi 4  /\wa 369  =wceq 1395  e.wcel 1818  =/=wne 2652  {crab 2811   cvv 3109   c0 3784  {csn 4029  domcdm 5004  "cima 5007  (class class class)co 6296   csupp 6918 This theorem is referenced by:  suppssdm  6931  suppun  6939  extmptsuppeq  6943  funsssuppss  6945  fczsupp0  6948  suppss  6949  suppssov1  6951  suppss2  6953  suppssfv  6955  supp0cosupp0  6958  imacosupp  6959  fsuppun  7868 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-8 1820  ax-9 1822  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435  ax-sep 4573  ax-nul 4581  ax-pow 4630  ax-pr 4691 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-eu 2286  df-mo 2287  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-ral 2812  df-rex 2813  df-rab 2816  df-v 3111  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-if 3942  df-sn 4030  df-pr 4032  df-op 4036  df-uni 4250  df-br 4453  df-opab 4511  df-xp 5010  df-dm 5014  df-iota 5556  df-fv 5601  df-ov 6299  df-oprab 6300  df-mpt2 6301  df-supp 6919
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