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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 5246 | . 2 ⊢ (𝐹:𝐴–onto→𝐵 → 𝐹:𝐴⟶𝐵) | |
2 | ffn 5174 | . 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 5023 ⟶wf 5024 –onto→wfo 5026 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-5 1382 ax-7 1383 ax-gen 1384 ax-ie1 1428 ax-ie2 1429 ax-8 1441 ax-11 1443 ax-4 1446 ax-17 1465 ax-i9 1469 ax-ial 1473 ax-i5r 1474 ax-ext 2071 |
This theorem depends on definitions: df-bi 116 df-nf 1396 df-sb 1694 df-clab 2076 df-cleq 2082 df-clel 2085 df-in 3006 df-ss 3013 df-f 5032 df-fo 5034 |
This theorem is referenced by: fodmrnu 5254 foun 5285 fo00 5302 foima2 5544 cbvfo 5578 cbvexfo 5579 foeqcnvco 5583 1stcof 5948 2ndcof 5949 1stexg 5952 2ndexg 5953 df1st2 5998 df2nd2 5999 1stconst 6000 2ndconst 6001 fidcenumlemrks 6716 fidcenumlemr 6718 ctm 6845 |
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