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Theorem fimass 5979
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 5383 . . 3 (𝐹𝑋) ⊆ ran 𝐹
21a1i 11 . 2 (𝐹:𝐴𝐵 → (𝐹𝑋) ⊆ ran 𝐹)
3 frn 5952 . 2 (𝐹:𝐴𝐵 → ran 𝐹𝐵)
42, 3sstrd 3577 1 (𝐹:𝐴𝐵 → (𝐹𝑋) ⊆ 𝐵)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wss 3539  ran crn 5029  cima 5031  wf 5786
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1712  ax-4 1727  ax-5 1826  ax-6 1874  ax-7 1921  ax-9 1985  ax-10 2005  ax-11 2020  ax-12 2032  ax-13 2232  ax-ext 2589  ax-sep 4703  ax-nul 4712  ax-pr 4828
This theorem depends on definitions:  df-bi 195  df-or 383  df-an 384  df-3an 1032  df-tru 1477  df-ex 1695  df-nf 1700  df-sb 1867  df-eu 2461  df-mo 2462  df-clab 2596  df-cleq 2602  df-clel 2605  df-nfc 2739  df-ral 2900  df-rex 2901  df-rab 2904  df-v 3174  df-dif 3542  df-un 3544  df-in 3546  df-ss 3553  df-nul 3874  df-if 4036  df-sn 4125  df-pr 4127  df-op 4131  df-br 4578  df-opab 4638  df-xp 5034  df-cnv 5036  df-dm 5038  df-rn 5039  df-res 5040  df-ima 5041  df-f 5794
This theorem is referenced by:  fissuni  8131  fipreima  8132  sge0f1o  39079  trlreslem  40909
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