Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  itg2l Structured version   Unicode version

Theorem itg2l 22428
 Description: Elementhood in the set of lower sums of the integral. (Contributed by Mario Carneiro, 28-Jun-2014.)
Hypothesis
Ref Expression
itg2val.1
Assertion
Ref Expression
itg2l
Distinct variable groups:   ,,   ,,
Allowed substitution hints:   (,)

Proof of Theorem itg2l
StepHypRef Expression
1 itg2val.1 . . 3
21eleq2i 2480 . 2
3 simpr 459 . . . . 5
4 fvex 5859 . . . . 5
53, 4syl6eqel 2498 . . . 4
65rexlimivw 2893 . . 3
7 eqeq1 2406 . . . . 5
87anbi2d 702 . . . 4
98rexbidv 2918 . . 3
106, 9elab3 3203 . 2
112, 10bitri 249 1
 Colors of variables: wff setvar class Syntax hints:   wb 184   wa 367   wceq 1405   wcel 1842  cab 2387  wrex 2755  cvv 3059   class class class wbr 4395   cdm 4823  cfv 5569   cofr 6520   cle 9659  citg1 22316 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1639  ax-4 1652  ax-5 1725  ax-6 1771  ax-7 1814  ax-10 1861  ax-11 1866  ax-12 1878  ax-13 2026  ax-ext 2380  ax-nul 4525 This theorem depends on definitions:  df-bi 185  df-or 368  df-an 369  df-tru 1408  df-ex 1634  df-nf 1638  df-sb 1764  df-eu 2242  df-clab 2388  df-cleq 2394  df-clel 2397  df-nfc 2552  df-ne 2600  df-ral 2759  df-rex 2760  df-v 3061  df-sbc 3278  df-dif 3417  df-un 3419  df-in 3421  df-ss 3428  df-nul 3739  df-sn 3973  df-pr 3975  df-uni 4192  df-iota 5533  df-fv 5577 This theorem is referenced by:  itg2lr  22429
 Copyright terms: Public domain W3C validator