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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 5907 | . 2 ⊢ (𝐹 “ 𝑋) ⊆ ran 𝐹 | |
2 | frn 6493 | . 2 ⊢ (𝐹:𝐴⟶𝐵 → ran 𝐹 ⊆ 𝐵) | |
3 | 1, 2 | sstrid 3926 | 1 ⊢ (𝐹:𝐴⟶𝐵 → (𝐹 “ 𝑋) ⊆ 𝐵) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ⊆ wss 3881 ran crn 5520 “ cima 5522 ⟶wf 6320 |
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 1911 ax-6 1970 ax-7 2015 ax-8 2113 ax-9 2121 ax-10 2142 ax-11 2158 ax-12 2175 ax-ext 2770 ax-sep 5167 ax-nul 5174 ax-pr 5295 |
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 2070 df-mo 2598 df-eu 2629 df-clab 2777 df-cleq 2791 df-clel 2870 df-nfc 2938 df-ral 3111 df-rex 3112 df-v 3443 df-dif 3884 df-un 3886 df-in 3888 df-ss 3898 df-nul 4244 df-if 4426 df-sn 4526 df-pr 4528 df-op 4532 df-br 5031 df-opab 5093 df-xp 5525 df-cnv 5527 df-dm 5529 df-rn 5530 df-res 5531 df-ima 5532 df-f 6328 |
This theorem is referenced by: fimacnv 6816 f1imaen2g 8553 domunsncan 8600 fissuni 8813 fipreima 8814 carduniima 9507 psgnunilem1 18613 fbasrn 22489 imaelfm 22556 wlkres 27460 trlreslem 27489 fimarab 30404 tocyccntz 30836 rhmimaidl 31017 nummin 32474 fimassd 41864 limsupvaluz 42350 sge0f1o 43021 fundcmpsurbijinjpreimafv 43924 fundcmpsurinjimaid 43928 |
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