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Theorem iccleub 10972
 Description: An element of a closed interval is less than or equal to its upper bound. (Contributed by Jeffrey Hankins, 14-Jul-2009.)
Assertion
Ref Expression
iccleub

Proof of Theorem iccleub
StepHypRef Expression
1 elicc1 10965 . . 3
2 simp3 960 . . 3
31, 2syl6bi 221 . 2
433impia 1151 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 360   w3a 937   wcel 1726   class class class wbr 4215  (class class class)co 6084  cxr 9124   cle 9126  cicc 10924 This theorem is referenced by:  oprpiece1res1  18981  ivthlem1  19353  isosctrlem1  20667  mblfinlem1  26255  ftc1cnnclem  26292  ftc2nc  26303  isosctrlem1ALT  29120 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-13 1728  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  ax-un 4704  ax-cnex 9051  ax-resscn 9052 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-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-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-ov 6087  df-oprab 6088  df-mpt2 6089  df-xr 9129  df-icc 10928
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