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Theorem ditgpos 22128
 Description: Value of the directed integral in the forward direction. (Contributed by Mario Carneiro, 13-Aug-2014.)
Hypothesis
Ref Expression
ditgpos.1
Assertion
Ref Expression
ditgpos _
Distinct variable groups:   ,   ,   ,
Allowed substitution hint:   ()

Proof of Theorem ditgpos
StepHypRef Expression
1 df-ditg 22119 . 2 _
2 ditgpos.1 . . 3
3 iftrue 3951 . . 3
42, 3syl 16 . 2
51, 4syl5eq 2520 1 _
 Colors of variables: wff setvar class Syntax hints:   wi 4   wceq 1379  cif 3945   class class class wbr 4453  (class class class)co 6295   cle 9641  cneg 9818  cioo 11541  citg 21895  _cdit 22118 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-10 1786  ax-11 1791  ax-12 1803  ax-13 1968  ax-ext 2445 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1382  df-ex 1597  df-nf 1600  df-sb 1712  df-clab 2453  df-cleq 2459  df-clel 2462  df-if 3946  df-ditg 22119 This theorem is referenced by:  ditgcl  22130  ditgswap  22131  ditgsplitlem  22132  ftc2ditglem  22314  itgsubstlem  22317  itgsubst  22318  ditgeqiooicc  31601  itgiccshift  31621  itgperiod  31622  fourierdlem82  31812
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