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Mirrors > Home > ILE Home > Th. List > frnd | GIF version |
Description: Deduction form of frn 5251. 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 5251 | . 2 ⊢ (𝐹:𝐴⟶𝐵 → ran 𝐹 ⊆ 𝐵) | |
3 | 1, 2 | syl 14 | 1 ⊢ (𝜑 → ran 𝐹 ⊆ 𝐵) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ⊆ wss 3041 ran crn 4510 ⟶wf 5089 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 |
This theorem depends on definitions: df-bi 116 df-f 5097 |
This theorem is referenced by: difinfsn 6953 ennnfonelemfun 11857 ennnfonelemf1 11858 tgrest 12265 resttopon 12267 rest0 12275 cnrest2r 12333 cnptoprest2 12336 lmss 12342 txbasval 12363 upxp 12368 uptx 12370 hmeores 12411 unirnblps 12518 unirnbl 12519 |
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