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Mirrors > Home > MPE Home > Th. List > fimass | Structured version Visualization version GIF version |
Description: The image of a class is a subset of its codomain. (Contributed by Glauco Siliprandi, 17-Aug-2020.) |
Ref | Expression |
---|---|
fimass | ⊢ (𝐹:𝐴⟶𝐵 → (𝐹 “ 𝑋) ⊆ 𝐵) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | imassrn 5933 | . 2 ⊢ (𝐹 “ 𝑋) ⊆ ran 𝐹 | |
2 | frn 6513 | . 2 ⊢ (𝐹:𝐴⟶𝐵 → ran 𝐹 ⊆ 𝐵) | |
3 | 1, 2 | sstrid 3975 | 1 ⊢ (𝐹:𝐴⟶𝐵 → (𝐹 “ 𝑋) ⊆ 𝐵) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ⊆ wss 3933 ran crn 5549 “ cima 5551 ⟶wf 6344 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1787 ax-4 1801 ax-5 1902 ax-6 1961 ax-7 2006 ax-8 2107 ax-9 2115 ax-10 2136 ax-11 2151 ax-12 2167 ax-ext 2790 ax-sep 5194 ax-nul 5201 ax-pr 5320 |
This theorem depends on definitions: df-bi 208 df-an 397 df-or 842 df-3an 1081 df-tru 1531 df-ex 1772 df-nf 1776 df-sb 2061 df-mo 2615 df-eu 2647 df-clab 2797 df-cleq 2811 df-clel 2890 df-nfc 2960 df-ral 3140 df-rex 3141 df-rab 3144 df-v 3494 df-dif 3936 df-un 3938 df-in 3940 df-ss 3949 df-nul 4289 df-if 4464 df-sn 4558 df-pr 4560 df-op 4564 df-br 5058 df-opab 5120 df-xp 5554 df-cnv 5556 df-dm 5558 df-rn 5559 df-res 5560 df-ima 5561 df-f 6352 |
This theorem is referenced by: fimacnv 6831 f1imaen2g 8558 domunsncan 8605 fissuni 8817 fipreima 8818 carduniima 9510 psgnunilem1 18550 fbasrn 22420 imaelfm 22487 wlkres 27379 trlreslem 27408 fimarab 30318 tocyccntz 30713 fimassd 41374 limsupvaluz 41865 sge0f1o 42541 fundcmpsurbijinjpreimafv 43444 fundcmpsurinjimaid 43448 |
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