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Theorem fimassd 41729
Description: The image of a class is a subset of its codomain. (Contributed by Glauco Siliprandi, 23-Oct-2021.)
Hypothesis
Ref Expression
fimassd.1 (𝜑𝐹:𝐴𝐵)
Assertion
Ref Expression
fimassd (𝜑 → (𝐹𝑋) ⊆ 𝐵)

Proof of Theorem fimassd
StepHypRef Expression
1 fimassd.1 . 2 (𝜑𝐹:𝐴𝐵)
2 fimass 6544 . 2 (𝐹:𝐴𝐵 → (𝐹𝑋) ⊆ 𝐵)
31, 2syl 17 1 (𝜑 → (𝐹𝑋) ⊆ 𝐵)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wss 3919  cima 5546  wf 6340
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 5190  ax-nul 5197  ax-pr 5318
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 3138  df-rex 3139  df-v 3482  df-dif 3922  df-un 3924  df-in 3926  df-ss 3936  df-nul 4277  df-if 4451  df-sn 4551  df-pr 4553  df-op 4557  df-br 5054  df-opab 5116  df-xp 5549  df-cnv 5551  df-dm 5553  df-rn 5554  df-res 5555  df-ima 5556  df-f 6348
This theorem is referenced by:  limsupval3  42200  limsupmnflem  42228  liminfval5  42273
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