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Mirrors > Home > MPE Home > Th. List > fofun | Structured version Visualization version 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 6821 | . 2 ⊢ (𝐹:𝐴–onto→𝐵 → 𝐹:𝐴⟶𝐵) | |
2 | 1 | ffund 6741 | 1 ⊢ (𝐹:𝐴–onto→𝐵 → Fun 𝐹) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 Fun wfun 6557 –onto→wfo 6561 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1792 ax-4 1806 ax-5 1908 ax-6 1965 ax-7 2005 ax-9 2116 ax-ext 2706 |
This theorem depends on definitions: df-bi 207 df-an 396 df-ex 1777 df-cleq 2727 df-ss 3980 df-fn 6566 df-f 6567 df-fo 6569 |
This theorem is referenced by: foco 6835 foimacnv 6866 resdif 6870 fococnv2 6875 focdmex 7979 fodomfi2 10098 fin1a2lem7 10444 brdom3 10566 1stf1 18248 1stf2 18249 2ndf1 18251 2ndf2 18252 1stfcl 18253 2ndfcl 18254 qtopcld 23737 qtopcmap 23743 elfm3 23974 bcthlem4 25375 uniiccdif 25627 bdayimaon 27753 nosupno 27763 noinfno 27778 bdayfun 27832 noeta2 27844 precsexlem10 28255 precsexlem11 28256 grporn 30550 xppreima 32662 fsuppcurry1 32743 fsuppcurry2 32744 qtophaus 33797 poimirlem26 37633 poimirlem27 37634 ovoliunnfl 37649 voliunnfl 37651 |
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