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Theorem measvnul 26329
Description: The measure of the empty set is always zero. (Contributed by Thierry Arnoux, 26-Dec-2016.)
Assertion
Ref Expression
measvnul

Proof of Theorem measvnul
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 measbase 26320 . . . 4
2 ismeas 26322 . . . 4
31, 2syl 16 . . 3
43ibi 235 . 2
54simp2d 986 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  <->wb 178  /\wa 362  /\w3a 950  =wceq 1687  e.wcel 1749  A.wral 2694   c0 3614  ~Pcpw 3837  U.cuni 4066  Disj_wdisj 4237   class class class wbr 4267  rancrn 4812  -->wf 5386  `cfv 5390  (class class class)co 6061   com 6446   cdom 7267  0cc0 9228   cpnf 9361   cicc 11248  sum*cesum 26192   csiga 26259   cmeas 26318
This theorem is referenced by:  measxun2  26333  measvunilem0  26336  measssd  26338  measinb  26344  measres  26345  measdivcstOLD  26347  measdivcst  26348  truae  26368  probnul  26500
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1586  ax-4 1597  ax-5 1661  ax-6 1701  ax-7 1721  ax-8 1751  ax-9 1753  ax-10 1768  ax-11 1773  ax-12 1785  ax-13 1934  ax-ext 2403  ax-sep 4388  ax-nul 4396  ax-pow 4442  ax-pr 4503  ax-un 6342
This theorem depends on definitions:  df-bi 179  df-or 363  df-an 364  df-3an 952  df-tru 1355  df-fal 1356  df-ex 1582  df-nf 1585  df-sb 1694  df-eu 2248  df-mo 2249  df-clab 2409  df-cleq 2415  df-clel 2418  df-nfc 2547  df-ne 2587  df-ral 2699  df-rex 2700  df-rab 2703  df-v 2953  df-sbc 3165  df-csb 3266  df-dif 3308  df-un 3310  df-in 3312  df-ss 3319  df-nul 3615  df-if 3769  df-pw 3839  df-sn 3859  df-pr 3860  df-op 3862  df-uni 4067  df-br 4268  df-opab 4326  df-mpt 4327  df-id 4607  df-xp 4817  df-rel 4818  df-cnv 4819  df-co 4820  df-dm 4821  df-rn 4822  df-iota 5353  df-fun 5392  df-fn 5393  df-f 5394  df-fv 5398  df-ov 6064  df-esum 26193  df-meas 26319
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