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Theorem imanonrel 43496
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 5712 . 2 ((𝐴𝐴) “ 𝐵) = ran ((𝐴𝐴) ↾ 𝐵)
2 resnonrel 43495 . . 3 ((𝐴𝐴) ↾ 𝐵) = ∅
32rneqi 5961 . 2 ran ((𝐴𝐴) ↾ 𝐵) = ran ∅
4 rn0 5949 . 2 ran ∅ = ∅
51, 3, 43eqtri 2766 1 ((𝐴𝐴) “ 𝐵) = ∅
Colors of variables: wff setvar class
Syntax hints:   = wceq 1537  cdif 3967  c0 4347  ccnv 5698  ran crn 5700  cres 5701  cima 5702
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1793  ax-4 1807  ax-5 1909  ax-6 1967  ax-7 2007  ax-8 2105  ax-9 2113  ax-10 2136  ax-11 2153  ax-12 2173  ax-ext 2705  ax-sep 5320  ax-nul 5327  ax-pr 5450
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 847  df-3an 1089  df-tru 1540  df-fal 1550  df-ex 1778  df-nf 1782  df-sb 2065  df-clab 2712  df-cleq 2726  df-clel 2813  df-rab 3439  df-v 3484  df-dif 3973  df-un 3975  df-in 3977  df-ss 3987  df-nul 4348  df-if 4549  df-sn 4649  df-pr 4651  df-op 4655  df-br 5170  df-opab 5232  df-xp 5705  df-rel 5706  df-cnv 5707  df-dm 5709  df-rn 5710  df-res 5711  df-ima 5712
This theorem is referenced by: (None)
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