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Mirrors > Home > ILE Home > Th. List > fofn | GIF version |
Description: An onto mapping is a function on its domain. (Contributed by NM, 16-Dec-2008.) |
Ref | Expression |
---|---|
fofn | ⊢ (𝐹:𝐴–onto→𝐵 → 𝐹 Fn 𝐴) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | fof 5126 | . 2 ⊢ (𝐹:𝐴–onto→𝐵 → 𝐹:𝐴⟶𝐵) | |
2 | ffn 5066 | . 2 ⊢ (𝐹:𝐴⟶𝐵 → 𝐹 Fn 𝐴) | |
3 | 1, 2 | syl 14 | 1 ⊢ (𝐹:𝐴–onto→𝐵 → 𝐹 Fn 𝐴) |
Colors of variables: wff set class |
Syntax hints: → wi 4 Fn wfn 4917 ⟶wf 4918 –onto→wfo 4920 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-11 1437 ax-4 1440 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 |
This theorem depends on definitions: df-bi 115 df-nf 1390 df-sb 1686 df-clab 2068 df-cleq 2074 df-clel 2077 df-in 2979 df-ss 2986 df-f 4926 df-fo 4928 |
This theorem is referenced by: fodmrnu 5134 foun 5165 fo00 5182 cbvfo 5445 cbvexfo 5446 foeqcnvco 5450 1stcof 5810 2ndcof 5811 1stexg 5814 2ndexg 5815 df1st2 5860 df2nd2 5861 1stconst 5862 2ndconst 5863 |
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