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Theorem tz6.12i 5780
 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 5771 . . . . 5
2 neeq1 2615 . . . . . . . 8
3 tz6.12-2 5748 . . . . . . . . . . 11
43necon1ai 2652 . . . . . . . . . 10
5 tz6.12c 5779 . . . . . . . . . 10
64, 5syl 16 . . . . . . . . 9
76biimpcd 217 . . . . . . . 8
82, 7sylbird 228 . . . . . . 7
98eqcoms 2445 . . . . . 6
10 neeq1 2615 . . . . . 6
11 breq2 4241 . . . . . 6
129, 10, 113imtr3d 260 . . . . 5
131, 12vtocle 3031 . . . 4
1413a1i 11 . . 3
15 neeq1 2615 . . 3
16 breq2 4241 . . 3
1714, 15, 163imtr3d 260 . 2
1817com12 30 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 178   wceq 1653  weu 2287   wne 2605  c0 3613   class class class wbr 4237  cfv 5483 This theorem is referenced by:  fvbr0  5781  fvclss  6009  dcomex  8358 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1668  ax-8 1689  ax-6 1746  ax-7 1751  ax-11 1763  ax-12 1953  ax-ext 2423  ax-nul 4363 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-eu 2291  df-clab 2429  df-cleq 2435  df-clel 2438  df-nfc 2567  df-ne 2607  df-ral 2716  df-rex 2717  df-rab 2720  df-v 2964  df-sbc 3168  df-dif 3309  df-un 3311  df-in 3313  df-ss 3320  df-nul 3614  df-if 3764  df-sn 3844  df-pr 3845  df-op 3847  df-uni 4040  df-br 4238  df-iota 5447  df-fv 5491
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