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Theorem tz6.12i 5869
 Description: Corollary of Theorem 6.12(2) of [TakeutiZaring] p. 27. (Contributed by Mario Carneiro, 17-Nov-2014.)
Assertion
Ref Expression
tz6.12i

Proof of Theorem tz6.12i
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 fvex 5859 . . . . 5
2 neeq1 2684 . . . . . . . 8
3 tz6.12-2 5840 . . . . . . . . . . 11
43necon1ai 2634 . . . . . . . . . 10
5 tz6.12c 5868 . . . . . . . . . 10
64, 5syl 17 . . . . . . . . 9
76biimpcd 224 . . . . . . . 8
82, 7sylbird 235 . . . . . . 7
98eqcoms 2414 . . . . . 6
10 neeq1 2684 . . . . . 6
11 breq2 4399 . . . . . 6
129, 10, 113imtr3d 267 . . . . 5
131, 12vtocle 3133 . . . 4
1413a1i 11 . . 3
15 neeq1 2684 . . 3
16 breq2 4399 . . 3
1714, 15, 163imtr3d 267 . 2
1817com12 29 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 184   wceq 1405  weu 2238   wne 2598  c0 3738   class class class wbr 4395  cfv 5569 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1639  ax-4 1652  ax-5 1725  ax-6 1771  ax-7 1814  ax-10 1861  ax-11 1866  ax-12 1878  ax-13 2026  ax-ext 2380  ax-nul 4525 This theorem depends on definitions:  df-bi 185  df-or 368  df-an 369  df-3an 976  df-tru 1408  df-ex 1634  df-nf 1638  df-sb 1764  df-eu 2242  df-clab 2388  df-cleq 2394  df-clel 2397  df-nfc 2552  df-ne 2600  df-ral 2759  df-rex 2760  df-rab 2763  df-v 3061  df-sbc 3278  df-dif 3417  df-un 3419  df-in 3421  df-ss 3428  df-nul 3739  df-if 3886  df-sn 3973  df-pr 3975  df-op 3979  df-uni 4192  df-br 4396  df-iota 5533  df-fv 5577 This theorem is referenced by:  fvbr0  5870  fvclss  6135  dcomex  8859
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