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Theorem itg2lr 22262
 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 2457 . . 3
2 breq1 4459 . . . . 5
3 fveq2 5872 . . . . . 6
43eqeq2d 2471 . . . . 5
52, 4anbi12d 710 . . . 4
65rspcev 3210 . . 3
71, 6mpanr2 684 . 2
8 itg2val.1 . . 3
98itg2l 22261 . 2
107, 9sylibr 212 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wa 369   wceq 1395   wcel 1819  cab 2442  wrex 2808   class class class wbr 4456   cdm 5008  cfv 5594   cofr 6538   cle 9646  citg1 22149 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1619  ax-4 1632  ax-5 1705  ax-6 1748  ax-7 1791  ax-10 1838  ax-11 1843  ax-12 1855  ax-13 2000  ax-ext 2435  ax-nul 4586 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1614  df-nf 1618  df-sb 1741  df-eu 2287  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-ral 2812  df-rex 2813  df-rab 2816  df-v 3111  df-sbc 3328  df-dif 3474  df-un 3476  df-in 3478  df-ss 3485  df-nul 3794  df-if 3945  df-sn 4033  df-pr 4035  df-op 4039  df-uni 4252  df-br 4457  df-iota 5557  df-fv 5602 This theorem is referenced by:  itg2ub  22265
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