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Theorem fntp 5634
 Description: A function with a domain of three elements. (Contributed by NM, 14-Sep-2011.) (Revised by Mario Carneiro, 26-Apr-2015.)
Hypotheses
Ref Expression
fntp.1
fntp.2
fntp.3
fntp.4
fntp.5
fntp.6
Assertion
Ref Expression
fntp

Proof of Theorem fntp
StepHypRef Expression
1 fntp.1 . . 3
2 fntp.2 . . 3
3 fntp.3 . . 3
4 fntp.4 . . 3
5 fntp.5 . . 3
6 fntp.6 . . 3
71, 2, 3, 4, 5, 6funtp 5630 . 2
84, 5, 6dmtpop 5474 . . 3
98a1i 11 . 2
10 df-fn 5581 . 2
117, 9, 10sylanbrc 664 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   w3a 974   wceq 1383   wcel 1804   wne 2638  cvv 3095  ctp 4018  cop 4020   cdm 4989   wfun 5572   wfn 5573 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1605  ax-4 1618  ax-5 1691  ax-6 1734  ax-7 1776  ax-9 1808  ax-10 1823  ax-11 1828  ax-12 1840  ax-13 1985  ax-ext 2421  ax-sep 4558  ax-nul 4566  ax-pr 4676 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 976  df-tru 1386  df-ex 1600  df-nf 1604  df-sb 1727  df-eu 2272  df-mo 2273  df-clab 2429  df-cleq 2435  df-clel 2438  df-nfc 2593  df-ne 2640  df-ral 2798  df-rex 2799  df-rab 2802  df-v 3097  df-dif 3464  df-un 3466  df-in 3468  df-ss 3475  df-nul 3771  df-if 3927  df-sn 4015  df-pr 4017  df-tp 4019  df-op 4021  df-br 4438  df-opab 4496  df-id 4785  df-xp 4995  df-rel 4996  df-cnv 4997  df-co 4998  df-dm 4999  df-fun 5580  df-fn 5581 This theorem is referenced by:  rabren3dioph  30724
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