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Theorem itg2l 19611
 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 2499 . 2
3 simpr 448 . . . . 5
4 fvex 5734 . . . . 5
53, 4syl6eqel 2523 . . . 4
65rexlimivw 2818 . . 3
7 eqeq1 2441 . . . . 5
87anbi2d 685 . . . 4
98rexbidv 2718 . . 3
106, 9elab3 3081 . 2
112, 10bitri 241 1
 Colors of variables: wff set class Syntax hints:   wb 177   wa 359   wceq 1652   wcel 1725  cab 2421  wrex 2698  cvv 2948   class class class wbr 4204   cdm 4870  cfv 5446   cofr 6296   cle 9111  citg1 19497 This theorem is referenced by:  itg2lr  19612 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416  ax-nul 4330 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-eu 2284  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ne 2600  df-ral 2702  df-rex 2703  df-v 2950  df-sbc 3154  df-dif 3315  df-un 3317  df-in 3319  df-ss 3326  df-nul 3621  df-sn 3812  df-pr 3813  df-uni 4008  df-iota 5410  df-fv 5454
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