![]() |
Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
|
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 5454 | . 2 ⊢ (𝐹:𝐴–onto→𝐵 → 𝐹:𝐴⟶𝐵) | |
2 | ffn 5381 | . 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 5227 ⟶wf 5228 –onto→wfo 5230 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-11 1517 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-ext 2171 |
This theorem depends on definitions: df-bi 117 df-nf 1472 df-sb 1774 df-clab 2176 df-cleq 2182 df-clel 2185 df-in 3150 df-ss 3157 df-f 5236 df-fo 5238 |
This theorem is referenced by: fodmrnu 5462 foun 5496 fo00 5513 foelcdmi 5585 foima2 5769 cbvfo 5803 cbvexfo 5804 foeqcnvco 5808 canth 5846 1stcof 6183 2ndcof 6184 1stexg 6187 2ndexg 6188 df1st2 6239 df2nd2 6240 1stconst 6241 2ndconst 6242 fidcenumlemrks 6977 fidcenumlemr 6979 ctm 7133 suplocexprlemell 7737 ennnfonelemhf1o 12459 ennnfonelemrn 12465 imasaddfnlemg 12784 imasgrp2 13045 imasrng 13303 imasring 13407 upxp 14209 uptx 14211 cnmpt1st 14225 cnmpt2nd 14226 pw1nct 15190 |
Copyright terms: Public domain | W3C validator |