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Theorem fvtp3 6126
 Description: The third value of a function with a domain of three elements. (Contributed by NM, 14-Sep-2011.)
Hypotheses
Ref Expression
fvtp3.1
fvtp3.4
Assertion
Ref Expression
fvtp3

Proof of Theorem fvtp3
StepHypRef Expression
1 tprot 4093 . . 3
21fveq1i 5880 . 2
3 necom 2694 . . . 4
4 fvtp3.1 . . . . 5
5 fvtp3.4 . . . . 5
64, 5fvtp2 6125 . . . 4
73, 6sylan2b 478 . . 3
87ancoms 455 . 2
92, 8syl5eq 2476 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wa 371   wceq 1438   wcel 1869   wne 2619  cvv 3082  ctp 4001  cop 4003  cfv 5599 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1666  ax-4 1679  ax-5 1749  ax-6 1795  ax-7 1840  ax-8 1871  ax-9 1873  ax-10 1888  ax-11 1893  ax-12 1906  ax-13 2054  ax-ext 2401  ax-sep 4544  ax-nul 4553  ax-pow 4600  ax-pr 4658 This theorem depends on definitions:  df-bi 189  df-or 372  df-an 373  df-3or 984  df-3an 985  df-tru 1441  df-ex 1661  df-nf 1665  df-sb 1788  df-eu 2270  df-mo 2271  df-clab 2409  df-cleq 2415  df-clel 2418  df-nfc 2573  df-ne 2621  df-ral 2781  df-rex 2782  df-rab 2785  df-v 3084  df-sbc 3301  df-dif 3440  df-un 3442  df-in 3444  df-ss 3451  df-nul 3763  df-if 3911  df-sn 3998  df-pr 4000  df-tp 4002  df-op 4004  df-uni 4218  df-br 4422  df-opab 4481  df-id 4766  df-xp 4857  df-rel 4858  df-cnv 4859  df-co 4860  df-dm 4861  df-res 4863  df-iota 5563  df-fun 5601  df-fv 5607 This theorem is referenced by:  wlkntrllem2  25282  constr3lem5  25368  rabren3dioph  35583  nnsum4primesodd  38609  nnsum4primesoddALTV  38610
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