![]() |
Mathbox for Scott Fenton |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > MPE Home > Th. List > Mathboxes > bdaydm | Structured version Visualization version GIF version |
Description: The birthday function's domain is No . (Contributed by Scott Fenton, 14-Jun-2011.) |
Ref | Expression |
---|---|
bdaydm | ⊢ dom bday = No |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bdayfo 33295 | . . 3 ⊢ bday : No –onto→On | |
2 | fof 6565 | . . 3 ⊢ ( bday : No –onto→On → bday : No ⟶On) | |
3 | 1, 2 | ax-mp 5 | . 2 ⊢ bday : No ⟶On |
4 | 3 | fdmi 6498 | 1 ⊢ dom bday = No |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1538 dom cdm 5519 Oncon0 6159 ⟶wf 6320 –onto→wfo 6322 No csur 33260 bday cbday 33262 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1797 ax-4 1811 ax-5 1911 ax-6 1970 ax-7 2015 ax-8 2113 ax-9 2121 ax-10 2142 ax-11 2158 ax-12 2175 ax-ext 2770 ax-rep 5154 ax-sep 5167 ax-nul 5174 ax-pr 5295 ax-un 7441 |
This theorem depends on definitions: df-bi 210 df-an 400 df-or 845 df-3or 1085 df-3an 1086 df-tru 1541 df-ex 1782 df-nf 1786 df-sb 2070 df-mo 2598 df-eu 2629 df-clab 2777 df-cleq 2791 df-clel 2870 df-nfc 2938 df-ne 2988 df-ral 3111 df-rex 3112 df-reu 3113 df-rab 3115 df-v 3443 df-sbc 3721 df-csb 3829 df-dif 3884 df-un 3886 df-in 3888 df-ss 3898 df-pss 3900 df-nul 4244 df-if 4426 df-pw 4499 df-sn 4526 df-pr 4528 df-tp 4530 df-op 4532 df-uni 4801 df-iun 4883 df-br 5031 df-opab 5093 df-mpt 5111 df-tr 5137 df-id 5425 df-eprel 5430 df-po 5438 df-so 5439 df-fr 5478 df-we 5480 df-xp 5525 df-rel 5526 df-cnv 5527 df-co 5528 df-dm 5529 df-rn 5530 df-res 5531 df-ima 5532 df-ord 6162 df-on 6163 df-suc 6165 df-iota 6283 df-fun 6326 df-fn 6327 df-f 6328 df-f1 6329 df-fo 6330 df-f1o 6331 df-fv 6332 df-1o 8085 df-no 33263 df-bday 33265 |
This theorem is referenced by: nocvxminlem 33360 nocvxmin 33361 |
Copyright terms: Public domain | W3C validator |