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Theorem itg2lr 19614
 Description: Sufficient condition for elementhood in the set . (Contributed by Mario Carneiro, 28-Jun-2014.)
Hypothesis
Ref Expression
itg2val.1
Assertion
Ref Expression
itg2lr
Distinct variable groups:   ,,   ,,
Allowed substitution hints:   (,)

Proof of Theorem itg2lr
StepHypRef Expression
1 eqid 2435 . . 3
2 breq1 4207 . . . . 5
3 fveq2 5720 . . . . . 6
43eqeq2d 2446 . . . . 5
52, 4anbi12d 692 . . . 4
65rspcev 3044 . . 3
71, 6mpanr2 666 . 2
8 itg2val.1 . . 3
98itg2l 19613 . 2
107, 9sylibr 204 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 359   wceq 1652   wcel 1725  cab 2421  wrex 2698   class class class wbr 4204   cdm 4870  cfv 5446   cofr 6296   cle 9113  citg1 19499 This theorem is referenced by:  itg2ub  19617 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-3an 938  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-rab 2706  df-v 2950  df-sbc 3154  df-dif 3315  df-un 3317  df-in 3319  df-ss 3326  df-nul 3621  df-if 3732  df-sn 3812  df-pr 3813  df-op 3815  df-uni 4008  df-br 4205  df-iota 5410  df-fv 5454
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