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Mirrors > Home > MPE Home > Th. List > bdayfn | Structured version Visualization version GIF version |
Description: The birthday function is a function over No . (Contributed by Scott Fenton, 30-Jun-2011.) |
Ref | Expression |
---|---|
bdayfn | ⊢ bday Fn No |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bdayfo 27704 | . 2 ⊢ bday : No –onto→On | |
2 | fofn 6809 | . 2 ⊢ ( bday : No –onto→On → bday Fn No ) | |
3 | 1, 2 | ax-mp 5 | 1 ⊢ bday Fn No |
Colors of variables: wff setvar class |
Syntax hints: Oncon0 6368 Fn wfn 6541 –onto→wfo 6544 No csur 27666 bday cbday 27668 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1790 ax-4 1804 ax-5 1906 ax-6 1964 ax-7 2004 ax-8 2101 ax-9 2109 ax-10 2130 ax-11 2147 ax-12 2167 ax-ext 2697 ax-sep 5296 ax-nul 5303 ax-pow 5361 ax-pr 5425 ax-un 7738 |
This theorem depends on definitions: df-bi 206 df-an 395 df-or 846 df-3an 1086 df-tru 1537 df-fal 1547 df-ex 1775 df-nf 1779 df-sb 2061 df-mo 2529 df-eu 2558 df-clab 2704 df-cleq 2718 df-clel 2803 df-nfc 2878 df-ne 2931 df-ral 3052 df-rex 3061 df-rab 3420 df-v 3464 df-dif 3949 df-un 3951 df-in 3953 df-ss 3963 df-nul 4323 df-if 4524 df-pw 4599 df-sn 4624 df-pr 4626 df-op 4630 df-uni 4906 df-br 5146 df-opab 5208 df-mpt 5229 df-id 5572 df-xp 5680 df-rel 5681 df-cnv 5682 df-co 5683 df-dm 5684 df-rn 5685 df-suc 6374 df-fun 6548 df-fn 6549 df-f 6550 df-fo 6552 df-1o 8488 df-no 27669 df-bday 27671 |
This theorem is referenced by: nocvxmin 27805 eqscut2 27833 scutun12 27837 scutbdaybnd 27842 scutbdaybnd2 27843 scutbdaylt 27845 bday1s 27858 cuteq0 27859 madebdaylemlrcut 27919 cofcut1 27934 cofcutr 27938 lrrecfr 27954 n0sbday 28317 |
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