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Mathbox for Glauco Siliprandi |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > frnd | Structured version Visualization version GIF version |
Description: The range of a mapping. (Contributed by Glauco Siliprandi, 26-Jun-2021.) |
Ref | Expression |
---|---|
frnd.1 | ⊢ (𝜑 → 𝐹:𝐴⟶𝐵) |
Ref | Expression |
---|---|
frnd | ⊢ (𝜑 → ran 𝐹 ⊆ 𝐵) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | frnd.1 | . 2 ⊢ (𝜑 → 𝐹:𝐴⟶𝐵) | |
2 | frn 6193 | . 2 ⊢ (𝐹:𝐴⟶𝐵 → ran 𝐹 ⊆ 𝐵) | |
3 | 1, 2 | syl 17 | 1 ⊢ (𝜑 → ran 𝐹 ⊆ 𝐵) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ⊆ wss 3723 ran crn 5250 ⟶wf 6027 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 |
This theorem depends on definitions: df-bi 197 df-an 383 df-f 6035 |
This theorem is referenced by: climinf2lem 40456 limsupvaluz2 40488 supcnvlimsup 40490 limsupgtlem 40527 preimaioomnf 41449 smfco 41529 |
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