Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  ditgpos Unicode version

Theorem ditgpos 21731
 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:   ,   ,   ,

Proof of Theorem ditgpos
StepHypRef Expression
1 df-ditg 21722 . 2
2 ditgpos.1 . . 3
3 iftrue 3911 . . 3
42, 3syl 16 . 2
51, 4syl5eq 2507 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  =wceq 1370  ifcif 3905   class class class wbr 4409  (class class class)co 6222   cle 9556  -ucneg 9733   cioo 11439  S.citg 21498  S_cdit 21721 This theorem is referenced by:  ditgcl  21733  ditgswap  21734  ditgsplitlem  21735  ftc2ditglem  21917  itgsubstlem  21920  itgsubst  21921  ditgeqiooicc  30507  itgiccshift  30527  itgperiod  30528  fourierdlem82  30718 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-5 1671  ax-6 1710  ax-7 1730  ax-10 1777  ax-11 1782  ax-12 1794  ax-13 1955  ax-ext 2432 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1373  df-ex 1588  df-nf 1591  df-sb 1703  df-clab 2440  df-cleq 2446  df-clel 2449  df-if 3906  df-ditg 21722
 Copyright terms: Public domain W3C validator