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Theorem bdayrn 25634
Description: The birthday function's range is  On (Contributed by Scott Fenton, 14-Jun-2011.)
Assertion
Ref Expression
bdayrn  |-  ran  bday  =  On

Proof of Theorem bdayrn
StepHypRef Expression
1 bdayfo 25632 . 2  |-  bday : No -onto-> On
2 forn 5658 . 2  |-  ( bday
: No -onto-> On  ->  ran 
bday  =  On )
31, 2ax-mp 8 1  |-  ran  bday  =  On
Colors of variables: wff set class
Syntax hints:    = wceq 1653   Oncon0 4583   ran crn 4881   -onto->wfo 5454   Nocsur 25597   bdaycbday 25599
This theorem is referenced by:  bdayelon  25637  nocvxminlem  25647  nocvxmin  25648  nobndlem1  25649  nobndlem2  25650
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-13 1728  ax-14 1730  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419  ax-rep 4322  ax-sep 4332  ax-nul 4340  ax-pr 4405  ax-un 4703
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3or 938  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-eu 2287  df-mo 2288  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ne 2603  df-ral 2712  df-rex 2713  df-reu 2714  df-rab 2716  df-v 2960  df-sbc 3164  df-csb 3254  df-dif 3325  df-un 3327  df-in 3329  df-ss 3336  df-pss 3338  df-nul 3631  df-if 3742  df-pw 3803  df-sn 3822  df-pr 3823  df-tp 3824  df-op 3825  df-uni 4018  df-iun 4097  df-br 4215  df-opab 4269  df-mpt 4270  df-tr 4305  df-eprel 4496  df-id 4500  df-po 4505  df-so 4506  df-fr 4543  df-we 4545  df-ord 4586  df-on 4587  df-suc 4589  df-xp 4886  df-rel 4887  df-cnv 4888  df-co 4889  df-dm 4890  df-rn 4891  df-res 4892  df-ima 4893  df-iota 5420  df-fun 5458  df-fn 5459  df-f 5460  df-f1 5461  df-fo 5462  df-f1o 5463  df-fv 5464  df-1o 6726  df-no 25600  df-bday 25602
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