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Theorem tz6.12i 5510
 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 5500 . . . . 5
2 neeq1 2455 . . . . . . . 8
3 tz6.12-2 5508 . . . . . . . . . . 11
43necon1ai 2489 . . . . . . . . . 10
5 tz6.12c 5509 . . . . . . . . . 10
64, 5syl 15 . . . . . . . . 9
76biimpcd 215 . . . . . . . 8
82, 7sylbird 226 . . . . . . 7
98eqcoms 2287 . . . . . 6
10 neeq1 2455 . . . . . 6
11 breq2 4028 . . . . . 6
129, 10, 113imtr3d 258 . . . . 5
131, 12vtocle 2858 . . . 4
1413a1i 10 . . 3
15 neeq1 2455 . . 3
16 breq2 4028 . . 3
1714, 15, 163imtr3d 258 . 2
1817com12 27 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 176   wceq 1623  weu 2144   wne 2447  c0 3456   class class class wbr 4024  cfv 5221 This theorem is referenced by:  fvbr0  5511  fvclss  5722  dcomex  8069 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1636  ax-8 1644  ax-13 1687  ax-14 1689  ax-6 1704  ax-7 1709  ax-11 1716  ax-12 1868  ax-ext 2265  ax-sep 4142  ax-nul 4150  ax-pr 4213  ax-un 4511 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1631  df-eu 2148  df-mo 2149  df-clab 2271  df-cleq 2277  df-clel 2280  df-nfc 2409  df-ne 2449  df-ral 2549  df-rex 2550  df-rab 2553  df-v 2791  df-sbc 2993  df-dif 3156  df-un 3158  df-in 3160  df-ss 3167  df-nul 3457  df-if 3567  df-sn 3647  df-pr 3648  df-op 3650  df-uni 3829  df-br 4025  df-opab 4079  df-xp 4694  df-cnv 4696  df-dm 4698  df-rn 4699  df-res 4700  df-ima 4701  df-fv 5229
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