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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 5353 | . 2 ⊢ (𝐹:𝐴–onto→𝐵 → 𝐹:𝐴⟶𝐵) | |
2 | ffn 5280 | . 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 5126 ⟶wf 5127 –onto→wfo 5129 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-5 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-11 1485 ax-4 1488 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 |
This theorem depends on definitions: df-bi 116 df-nf 1438 df-sb 1737 df-clab 2127 df-cleq 2133 df-clel 2136 df-in 3082 df-ss 3089 df-f 5135 df-fo 5137 |
This theorem is referenced by: fodmrnu 5361 foun 5394 fo00 5411 foima2 5661 cbvfo 5694 cbvexfo 5695 foeqcnvco 5699 1stcof 6069 2ndcof 6070 1stexg 6073 2ndexg 6074 df1st2 6124 df2nd2 6125 1stconst 6126 2ndconst 6127 fidcenumlemrks 6849 fidcenumlemr 6851 ctm 7002 suplocexprlemell 7545 ennnfonelemhf1o 11962 ennnfonelemrn 11968 upxp 12480 uptx 12482 cnmpt1st 12496 cnmpt2nd 12497 pw1nct 13371 |
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