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Theorem ditgex 19770
 Description: A directed integral is a set. (Contributed by Mario Carneiro, 7-Sep-2014.)
Assertion
Ref Expression
ditgex _

Proof of Theorem ditgex
StepHypRef Expression
1 df-ditg 19765 . 2 _
2 itgex 19691 . . 3
3 negex 9335 . . 3
42, 3ifex 3821 . 2
51, 4eqeltri 2512 1 _
 Colors of variables: wff set class Syntax hints:   wcel 1727  cvv 2962  cif 3763   class class class wbr 4237  (class class class)co 6110   cle 9152  cneg 9323  cioo 10947  citg 19541  _cdit 19764 This theorem is referenced by:  itgsubstlem  19963 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 1668  ax-8 1689  ax-6 1746  ax-7 1751  ax-11 1763  ax-12 1953  ax-ext 2423  ax-nul 4363 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-eu 2291  df-clab 2429  df-cleq 2435  df-clel 2438  df-nfc 2567  df-ne 2607  df-ral 2716  df-rex 2717  df-v 2964  df-sbc 3168  df-dif 3309  df-un 3311  df-in 3313  df-ss 3320  df-nul 3614  df-if 3764  df-sn 3844  df-pr 3845  df-uni 4040  df-iota 5447  df-fv 5491  df-ov 6113  df-neg 9325  df-sum 12511  df-itg 19546  df-ditg 19765
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