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Mirrors > Home > MPE Home > Th. List > fofn | Structured version Visualization version 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 6820 | . 2 ⊢ (𝐹:𝐴–onto→𝐵 → 𝐹:𝐴⟶𝐵) | |
2 | 1 | ffnd 6737 | 1 ⊢ (𝐹:𝐴–onto→𝐵 → 𝐹 Fn 𝐴) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 Fn wfn 6557 –onto→wfo 6560 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1791 ax-4 1805 ax-5 1907 ax-6 1964 ax-7 2004 ax-9 2115 ax-ext 2705 |
This theorem depends on definitions: df-bi 207 df-an 396 df-ex 1776 df-cleq 2726 df-ss 3979 df-f 6566 df-fo 6568 |
This theorem is referenced by: fodmrnu 6828 foun 6866 fo00 6884 foelcdmi 6969 cbvfo 7308 foeqcnvco 7319 canth 7384 br1steqg 8034 br2ndeqg 8035 1stcof 8042 2ndcof 8043 df1st2 8121 df2nd2 8122 1stconst 8123 2ndconst 8124 fsplit 8140 smoiso2 8407 fodomfi 9347 fodomfiOLD 9367 brwdom2 9610 fodomfi2 10097 fpwwe 10683 imasaddfnlem 17574 imasvscafn 17583 imasleval 17587 dmaf 18102 cdaf 18103 imasmnd2 18799 imasgrp2 19085 efgrelexlemb 19782 efgredeu 19784 imasrng 20194 imasring 20343 znf1o 21587 zzngim 21588 indlcim 21877 1stcfb 23468 upxp 23646 uptx 23648 cnmpt1st 23691 cnmpt2nd 23692 qtoptopon 23727 qtopcld 23736 qtopeu 23739 qtoprest 23740 imastopn 23743 qtophmeo 23840 elfm3 23973 uniiccdif 25626 dirith 27587 nosupno 27762 nosupbday 27764 noinfno 27777 noinfbday 27779 noetasuplem4 27795 noetainflem4 27799 bdayfn 27832 grporn 30549 0vfval 30634 foresf1o 32531 2ndimaxp 32662 2ndresdju 32665 xppreima2 32667 1stpreimas 32720 1stpreima 32721 2ndpreima 32722 fsuppcurry1 32742 fsuppcurry2 32743 ffsrn 32746 gsummpt2d 33034 qusker 33356 imaslmod 33360 qtopt1 33795 qtophaus 33796 circcn 33798 cnre2csqima 33871 sigapildsys 34142 carsgclctunlem3 34301 fnbigcup 35882 filnetlem4 36363 ovoliunnfl 37648 voliunnfl 37650 volsupnfl 37651 ssnnf1octb 45136 nnfoctbdj 46411 fcoreslem4 47015 fcoresf1 47018 fargshiftfo 47366 |
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