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Theorem tz6.12i 5891
 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 5881 . . . . 5
2 neeq1 2738 . . . . . . . 8
3 tz6.12-2 5862 . . . . . . . . . . 11
43necon1ai 2688 . . . . . . . . . 10
5 tz6.12c 5890 . . . . . . . . . 10
64, 5syl 16 . . . . . . . . 9
76biimpcd 224 . . . . . . . 8
82, 7sylbird 235 . . . . . . 7
98eqcoms 2469 . . . . . 6
10 neeq1 2738 . . . . . 6
11 breq2 4456 . . . . . 6
129, 10, 113imtr3d 267 . . . . 5
131, 12vtocle 3183 . . . 4
1413a1i 11 . . 3
15 neeq1 2738 . . 3
16 breq2 4456 . . 3
1714, 15, 163imtr3d 267 . 2
1817com12 31 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  <->wb 184  =wceq 1395  E!weu 2282  =/=wne 2652   c0 3784   class class class wbr 4452  `cfv 5593 This theorem is referenced by:  fvbr0  5892  fvclss  6154  dcomex  8848 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435  ax-nul 4581 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-eu 2286  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 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-if 3942  df-sn 4030  df-pr 4032  df-op 4036  df-uni 4250  df-br 4453  df-iota 5556  df-fv 5601
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