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Theorem flval 11931
 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 4456 . . . 4
2 breq1 4455 . . . 4
31, 2anbi12d 710 . . 3
43riotabidv 6259 . 2
5 df-fl 11929 . 2
6 riotaex 6261 . 2
74, 5, 6fvmpt 5956 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  /\wa 369  =wceq 1395  e.wcel 1818   class class class wbr 4452  cfv 5593  iota_crio 6256  (class class class)co 6296   cr 9512  1`c1 9514   caddc 9516   clt 9649   cle 9650   cz 10889   cfl 11927 This theorem is referenced by:  flcl  11932  fllelt  11934  flflp1  11944  flbi  11952  dfceil2  11968  ltflcei  30043 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-9 1822  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435  ax-sep 4573  ax-nul 4581  ax-pr 4691 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-eu 2286  df-mo 2287  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-ral 2812  df-rex 2813  df-rab 2816  df-v 3111  df-sbc 3328  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-if 3942  df-sn 4030  df-pr 4032  df-op 4036  df-uni 4250  df-br 4453  df-opab 4511  df-mpt 4512  df-id 4800  df-xp 5010  df-rel 5011  df-cnv 5012  df-co 5013  df-dm 5014  df-iota 5556  df-fun 5595  df-fv 5601  df-riota 6257  df-fl 11929
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