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Theorem abelthlem7a 19829
 Description: Lemma for abelth 19833. (Contributed by Mario Carneiro, 8-May-2015.)
Hypotheses
Ref Expression
abelth.1
abelth.2
abelth.3
abelth.4
abelth.5
abelth.6
abelth.7
abelthlem6.1
Assertion
Ref Expression
abelthlem7a
Distinct variable groups:   ,,,   ,,,   ,,,   ,,   ,,
Allowed substitution hints:   ()   ()   (,,)

Proof of Theorem abelthlem7a
StepHypRef Expression
1 abelthlem6.1 . . 3
2 eldifi 3311 . . 3
31, 2syl 15 . 2
4 oveq2 5882 . . . . 5
54fveq2d 5545 . . . 4
6 fveq2 5541 . . . . . 6
76oveq2d 5890 . . . . 5
87oveq2d 5890 . . . 4
95, 8breq12d 4052 . . 3
10 abelth.5 . . 3
119, 10elrab2 2938 . 2
123, 11sylib 188 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 358   wceq 1632   wcel 1696  crab 2560   cdif 3162  csn 3653   class class class wbr 4039   cmpt 4093   cdm 4705  wf 5267  cfv 5271  (class class class)co 5874  cc 8751  cr 8752  cc0 8753  c1 8754   caddc 8756   cmul 8758   cle 8884   cmin 9053  cn0 9981   cseq 11062  cexp 11120  cabs 11735   cli 11974  csu 12174 This theorem is referenced by:  abelthlem7  19830 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-rex 2562  df-rab 2565  df-v 2803  df-dif 3168  df-un 3170  df-in 3172  df-ss 3179  df-nul 3469  df-if 3579  df-sn 3659  df-pr 3660  df-op 3662  df-uni 3844  df-br 4040  df-iota 5235  df-fv 5279  df-ov 5877
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