MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  fimass Structured version   Visualization version   GIF version

Theorem fimass 6536
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 5921 . 2 (𝐹𝑋) ⊆ ran 𝐹
2 frn 6501 . 2 (𝐹:𝐴𝐵 → ran 𝐹𝐵)
31, 2sstrid 3962 1 (𝐹:𝐴𝐵 → (𝐹𝑋) ⊆ 𝐵)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wss 3918  ran crn 5537  cima 5539  wf 6332
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1971  ax-7 2016  ax-8 2117  ax-9 2125  ax-10 2146  ax-11 2162  ax-12 2179  ax-ext 2796  ax-sep 5184  ax-nul 5191  ax-pr 5311
This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-3an 1086  df-tru 1541  df-ex 1782  df-nf 1786  df-sb 2071  df-mo 2624  df-eu 2655  df-clab 2803  df-cleq 2817  df-clel 2896  df-nfc 2964  df-ral 3137  df-rex 3138  df-rab 3141  df-v 3481  df-dif 3921  df-un 3923  df-in 3925  df-ss 3935  df-nul 4275  df-if 4449  df-sn 4549  df-pr 4551  df-op 4555  df-br 5048  df-opab 5110  df-xp 5542  df-cnv 5544  df-dm 5546  df-rn 5547  df-res 5548  df-ima 5549  df-f 6340
This theorem is referenced by:  fimacnv  6820  f1imaen2g  8553  domunsncan  8600  fissuni  8813  fipreima  8814  carduniima  9507  psgnunilem1  18610  fbasrn  22478  imaelfm  22545  wlkres  27449  trlreslem  27478  fimarab  30387  tocyccntz  30804  fimassd  41705  limsupvaluz  42192  sge0f1o  42863  fundcmpsurbijinjpreimafv  43766  fundcmpsurinjimaid  43770
  Copyright terms: Public domain W3C validator