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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 3976 | 1 ⊢ (𝐹:𝐴⟶𝐵 → (𝐹 “ 𝑋) ⊆ 𝐵) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ⊆ wss 3934 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 1790 ax-4 1804 ax-5 1905 ax-6 1964 ax-7 2009 ax-8 2110 ax-9 2118 ax-10 2139 ax-11 2154 ax-12 2170 ax-ext 2791 ax-sep 5194 ax-nul 5201 ax-pr 5320 |
This theorem depends on definitions: df-bi 209 df-an 399 df-or 844 df-3an 1084 df-tru 1534 df-ex 1775 df-nf 1779 df-sb 2064 df-mo 2616 df-eu 2648 df-clab 2798 df-cleq 2812 df-clel 2891 df-nfc 2961 df-ral 3141 df-rex 3142 df-rab 3145 df-v 3495 df-dif 3937 df-un 3939 df-in 3941 df-ss 3950 df-nul 4290 df-if 4466 df-sn 4560 df-pr 4562 df-op 4566 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 6832 f1imaen2g 8562 domunsncan 8609 fissuni 8821 fipreima 8822 carduniima 9514 psgnunilem1 18613 fbasrn 22484 imaelfm 22551 wlkres 27444 trlreslem 27473 fimarab 30382 tocyccntz 30779 fimassd 41488 limsupvaluz 41979 sge0f1o 42655 fundcmpsurbijinjpreimafv 43558 fundcmpsurinjimaid 43562 |
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