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Theorem fimass 6221
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 5618 . . 3 (𝐹𝑋) ⊆ ran 𝐹
21a1i 11 . 2 (𝐹:𝐴𝐵 → (𝐹𝑋) ⊆ ran 𝐹)
3 frn 6193 . 2 (𝐹:𝐴𝐵 → ran 𝐹𝐵)
42, 3sstrd 3760 1 (𝐹:𝐴𝐵 → (𝐹𝑋) ⊆ 𝐵)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wss 3721  ran crn 5250  cima 5252  wf 6027
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1869  ax-4 1884  ax-5 1990  ax-6 2056  ax-7 2092  ax-9 2153  ax-10 2173  ax-11 2189  ax-12 2202  ax-13 2407  ax-ext 2750  ax-sep 4912  ax-nul 4920  ax-pr 5034
This theorem depends on definitions:  df-bi 197  df-an 383  df-or 827  df-3an 1072  df-tru 1633  df-ex 1852  df-nf 1857  df-sb 2049  df-eu 2621  df-mo 2622  df-clab 2757  df-cleq 2763  df-clel 2766  df-nfc 2901  df-ral 3065  df-rex 3066  df-rab 3069  df-v 3351  df-dif 3724  df-un 3726  df-in 3728  df-ss 3735  df-nul 4062  df-if 4224  df-sn 4315  df-pr 4317  df-op 4321  df-br 4785  df-opab 4845  df-xp 5255  df-cnv 5257  df-dm 5259  df-rn 5260  df-res 5261  df-ima 5262  df-f 6035
This theorem is referenced by:  fissuni  8426  fipreima  8427  trlreslem  26830  fimassd  39944  limsupvaluz  40452  sge0f1o  41110
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