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Theorem itgvallem 19676
 Description: Substitution lemma. (Contributed by Mario Carneiro, 7-Jul-2014.) (Revised by Mario Carneiro, 23-Aug-2014.)
Hypothesis
Ref Expression
itgvallem.1
Assertion
Ref Expression
itgvallem
Distinct variable groups:   ,   ,
Allowed substitution hints:   (,)   (,)   (,)   ()

Proof of Theorem itgvallem
StepHypRef Expression
1 oveq2 6089 . . . . . . . . 9
2 itgvallem.1 . . . . . . . . 9
31, 2syl6eq 2484 . . . . . . . 8
43oveq2d 6097 . . . . . . 7
54fveq2d 5732 . . . . . 6
65breq2d 4224 . . . . 5
76anbi2d 685 . . . 4
8 eqidd 2437 . . . 4
97, 5, 8ifbieq12d 3761 . . 3
109mpteq2dv 4296 . 2
1110fveq2d 5732 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 359   wceq 1652   wcel 1725  cif 3739   class class class wbr 4212   cmpt 4266  cfv 5454  (class class class)co 6081  cr 8989  cc0 8990  ci 8992   cle 9121   cdiv 9677  cexp 11382  cre 11902  citg2 19508 This theorem is referenced by:  iblcnlem1  19679  itgcnlem  19681 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 2417 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-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ral 2710  df-rex 2711  df-rab 2714  df-v 2958  df-dif 3323  df-un 3325  df-in 3327  df-ss 3334  df-nul 3629  df-if 3740  df-sn 3820  df-pr 3821  df-op 3823  df-uni 4016  df-br 4213  df-opab 4267  df-mpt 4268  df-iota 5418  df-fv 5462  df-ov 6084
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