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Theorem imanonrel 41872
Description: An image under the non-relation part of a class is empty. (Contributed by RP, 22-Oct-2020.)
Assertion
Ref Expression
imanonrel ((𝐴𝐴) “ 𝐵) = ∅

Proof of Theorem imanonrel
StepHypRef Expression
1 df-ima 5647 . 2 ((𝐴𝐴) “ 𝐵) = ran ((𝐴𝐴) ↾ 𝐵)
2 resnonrel 41871 . . 3 ((𝐴𝐴) ↾ 𝐵) = ∅
32rneqi 5893 . 2 ran ((𝐴𝐴) ↾ 𝐵) = ran ∅
4 rn0 5882 . 2 ran ∅ = ∅
51, 3, 43eqtri 2769 1 ((𝐴𝐴) “ 𝐵) = ∅
Colors of variables: wff setvar class
Syntax hints:   = wceq 1542  cdif 3908  c0 4283  ccnv 5633  ran crn 5635  cres 5636  cima 5637
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-10 2138  ax-11 2155  ax-12 2172  ax-ext 2708  ax-sep 5257  ax-nul 5264  ax-pr 5385
This theorem depends on definitions:  df-bi 206  df-an 398  df-or 847  df-3an 1090  df-tru 1545  df-fal 1555  df-ex 1783  df-nf 1787  df-sb 2069  df-clab 2715  df-cleq 2729  df-clel 2815  df-rab 3409  df-v 3448  df-dif 3914  df-un 3916  df-in 3918  df-ss 3928  df-nul 4284  df-if 4488  df-sn 4588  df-pr 4590  df-op 4594  df-br 5107  df-opab 5169  df-xp 5640  df-rel 5641  df-cnv 5642  df-dm 5644  df-rn 5645  df-res 5646  df-ima 5647
This theorem is referenced by: (None)
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