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Mirrors > Home > ILE Home > Th. List > fofun | GIF version |
Description: An onto mapping is a function. (Contributed by NM, 29-Mar-2008.) |
Ref | Expression |
---|---|
fofun | ⊢ (𝐹:𝐴–onto→𝐵 → Fun 𝐹) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | fof 5404 | . 2 ⊢ (𝐹:𝐴–onto→𝐵 → 𝐹:𝐴⟶𝐵) | |
2 | ffun 5334 | . 2 ⊢ (𝐹:𝐴⟶𝐵 → Fun 𝐹) | |
3 | 1, 2 | syl 14 | 1 ⊢ (𝐹:𝐴–onto→𝐵 → Fun 𝐹) |
Colors of variables: wff set class |
Syntax hints: → wi 4 Fun wfun 5176 ⟶wf 5178 –onto→wfo 5180 |
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 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-11 1493 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-ext 2146 |
This theorem depends on definitions: df-bi 116 df-nf 1448 df-sb 1750 df-clab 2151 df-cleq 2157 df-clel 2160 df-in 3117 df-ss 3124 df-fn 5185 df-f 5186 df-fo 5188 |
This theorem is referenced by: foimacnv 5444 resdif 5448 fococnv2 5452 fornex 6075 ctssdccl 7067 suplocexprlem2b 7646 suplocexprlemmu 7650 suplocexprlemdisj 7652 suplocexprlemloc 7653 suplocexprlemub 7655 suplocexprlemlub 7656 ennnfonelemex 12290 ctinf 12306 |
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