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Theorem fimass 6548
Description: The image of a class is a subset of its codomain. (Contributed by Glauco Siliprandi, 17-Aug-2020.)
Assertion
Ref Expression
fimass (𝐹:𝐴𝐵 → (𝐹𝑋) ⊆ 𝐵)

Proof of Theorem fimass
StepHypRef Expression
1 imassrn 5933 . 2 (𝐹𝑋) ⊆ ran 𝐹
2 frn 6513 . 2 (𝐹:𝐴𝐵 → ran 𝐹𝐵)
31, 2sstrid 3975 1 (𝐹:𝐴𝐵 → (𝐹𝑋) ⊆ 𝐵)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wss 3933  ran crn 5549  cima 5551  wf 6344
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1787  ax-4 1801  ax-5 1902  ax-6 1961  ax-7 2006  ax-8 2107  ax-9 2115  ax-10 2136  ax-11 2151  ax-12 2167  ax-ext 2790  ax-sep 5194  ax-nul 5201  ax-pr 5320
This theorem depends on definitions:  df-bi 208  df-an 397  df-or 842  df-3an 1081  df-tru 1531  df-ex 1772  df-nf 1776  df-sb 2061  df-mo 2615  df-eu 2647  df-clab 2797  df-cleq 2811  df-clel 2890  df-nfc 2960  df-ral 3140  df-rex 3141  df-rab 3144  df-v 3494  df-dif 3936  df-un 3938  df-in 3940  df-ss 3949  df-nul 4289  df-if 4464  df-sn 4558  df-pr 4560  df-op 4564  df-br 5058  df-opab 5120  df-xp 5554  df-cnv 5556  df-dm 5558  df-rn 5559  df-res 5560  df-ima 5561  df-f 6352
This theorem is referenced by:  fimacnv  6831  f1imaen2g  8558  domunsncan  8605  fissuni  8817  fipreima  8818  carduniima  9510  psgnunilem1  18550  fbasrn  22420  imaelfm  22487  wlkres  27379  trlreslem  27408  fimarab  30318  tocyccntz  30713  fimassd  41374  limsupvaluz  41865  sge0f1o  42541  fundcmpsurbijinjpreimafv  43444  fundcmpsurinjimaid  43448
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