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Theorem fimass 6690
Description: The image of a class under a function with domain and codomain 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 6025 . 2 (𝐹𝑋) ⊆ ran 𝐹
2 frn 6676 . 2 (𝐹:𝐴𝐵 → ran 𝐹𝐵)
31, 2sstrid 3956 1 (𝐹:𝐴𝐵 → (𝐹𝑋) ⊆ 𝐵)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wss 3911  ran crn 5635  cima 5637  wf 6493
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-ext 2704  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-sb 2069  df-clab 2711  df-cleq 2725  df-clel 2811  df-ral 3062  df-rex 3071  df-rab 3407  df-v 3446  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-cnv 5642  df-dm 5644  df-rn 5645  df-res 5646  df-ima 5647  df-f 6501
This theorem is referenced by:  fimacnvOLD  7022  f1imaen2g  8958  domunsncan  9019  fissuni  9304  fipreima  9305  carduniima  10037  psgnunilem1  19280  fbasrn  23251  imaelfm  23318  wlkres  28660  trlreslem  28689  fimarab  31605  tocyccntz  32042  rhmimaidl  32254  nummin  33752  fimassd  43540  limsupvaluz  44035  sge0f1o  44709  fundcmpsurbijinjpreimafv  45685  fundcmpsurinjimaid  45689
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