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Theorem tz6.12i 5714
 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 5705 . . . . 5
2 neeq1 2579 . . . . . . . 8
3 tz6.12-2 5682 . . . . . . . . . . 11
43necon1ai 2613 . . . . . . . . . 10
5 tz6.12c 5713 . . . . . . . . . 10
64, 5syl 16 . . . . . . . . 9
76biimpcd 216 . . . . . . . 8
82, 7sylbird 227 . . . . . . 7
98eqcoms 2411 . . . . . 6
10 neeq1 2579 . . . . . 6
11 breq2 4180 . . . . . 6
129, 10, 113imtr3d 259 . . . . 5
131, 12vtocle 2989 . . . 4
1413a1i 11 . . 3
15 neeq1 2579 . . 3
16 breq2 4180 . . 3
1714, 15, 163imtr3d 259 . 2
1817com12 29 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wceq 1649  weu 2258   wne 2571  c0 3592   class class class wbr 4176  cfv 5417 This theorem is referenced by:  fvbr0  5715  fvclss  5943  dcomex  8287 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-6 1740  ax-7 1745  ax-11 1757  ax-12 1946  ax-ext 2389  ax-nul 4302 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-eu 2262  df-clab 2395  df-cleq 2401  df-clel 2404  df-nfc 2533  df-ne 2573  df-ral 2675  df-rex 2676  df-rab 2679  df-v 2922  df-sbc 3126  df-dif 3287  df-un 3289  df-in 3291  df-ss 3298  df-nul 3593  df-if 3704  df-sn 3784  df-pr 3785  df-op 3787  df-uni 3980  df-br 4177  df-iota 5381  df-fv 5425
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