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Theorem iccgelb 11610
 Description: An element of a closed interval is more than or equal to its lower bound (Contributed by Thierry Arnoux, 23-Dec-2016.)
Assertion
Ref Expression
iccgelb

Proof of Theorem iccgelb
StepHypRef Expression
1 elicc1 11602 . . . 4
21biimpa 484 . . 3
32simp2d 1009 . 2
433impa 1191 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  /\wa 369  /\w3a 973  e.wcel 1818   class class class wbr 4452  (class class class)co 6296   cxr 9648   cle 9650   cicc 11561 This theorem is referenced by:  supicc  11697  ttgcontlem1  24188  xrge0infss  27580  xrge0addgt0  27681  xrge0adddir  27682  esumcst  28071  esumpinfval  28079  oms0  28266  probmeasb  28369  areaquad  31184  lefldiveq  31482  eliccelioc  31561  iccintsng  31563  cncfiooiccre  31698  iblspltprt  31772  itgioocnicc  31776  itgspltprt  31778  itgiccshift  31779  fourierdlem1  31890  fourierdlem20  31909  fourierdlem24  31913  fourierdlem25  31914  fourierdlem27  31916  fourierdlem43  31932  fourierdlem44  31933  fourierdlem50  31939  fourierdlem51  31940  fourierdlem52  31941  fourierdlem64  31953  fourierdlem73  31962  fourierdlem76  31965  fourierdlem81  31970  fourierdlem92  31981  fourierdlem102  31991  fourierdlem103  31992  fourierdlem104  31993  fourierdlem114  32003 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-8 1820  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  ax-un 6592  ax-cnex 9569  ax-resscn 9570 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-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-ov 6299  df-oprab 6300  df-mpt2 6301  df-xr 9653  df-icc 11565
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