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Theorem flval 11208
 Description: Value of the floor (greatest integer) function. The floor of is the (unique) integer less than or equal to whose successor is strictly greater than . (Contributed by NM, 14-Nov-2004.) (Revised by Mario Carneiro, 2-Nov-2013.)
Assertion
Ref Expression
flval
Distinct variable group:   ,

Proof of Theorem flval
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 breq2 4219 . . . 4
2 breq1 4218 . . . 4
31, 2anbi12d 693 . . 3
43riotabidv 6554 . 2
5 df-fl 11207 . 2
6 riotaex 6556 . 2
74, 5, 6fvmpt 5809 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 360   wceq 1653   wcel 1726   class class class wbr 4215  cfv 5457  (class class class)co 6084  crio 6545  cr 8994  c1 8996   caddc 8998   clt 9125   cle 9126  cz 10287  cfl 11206 This theorem is referenced by:  flcl  11209  fllelt  11211  flbi  11228  ltflcei  26247  lxflflp1  26249 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-14 1730  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419  ax-sep 4333  ax-nul 4341  ax-pr 4406 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  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-dif 3325  df-un 3327  df-in 3329  df-ss 3336  df-nul 3631  df-if 3742  df-sn 3822  df-pr 3823  df-op 3825  df-uni 4018  df-br 4216  df-opab 4270  df-mpt 4271  df-id 4501  df-xp 4887  df-rel 4888  df-cnv 4889  df-co 4890  df-dm 4891  df-iota 5421  df-fun 5459  df-fv 5465  df-riota 6552  df-fl 11207
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