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Theorem ditgpos 19745
 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 19519 . 2 _
2 ditgpos.1 . . 3
3 iftrue 3747 . . 3
42, 3syl 16 . 2
51, 4syl5eq 2482 1 _
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1653  cif 3741   class class class wbr 4214  (class class class)co 6083   cle 9123  cneg 9294  cioo 10918  citg 19512  _cdit 19513 This theorem is referenced by:  ditgcl  19747  ditgswap  19748  ditgsplitlem  19749  ftc2ditglem  19931  itgsubstlem  19934  itgsubst  19935 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-if 3742  df-ditg 19519
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