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Theorem fconstfv 6133
 Description: A constant function expressed in terms of its functionality, domain, and value. See also fconst2 6127. (Contributed by NM, 27-Aug-2004.) (Proof shortened by OpenAI, 25-Mar-2020.)
Assertion
Ref Expression
fconstfv
Distinct variable groups:   ,   ,   ,

Proof of Theorem fconstfv
StepHypRef Expression
1 ffnfv 6057 . 2
2 fvex 5881 . . . . 5
32elsnc 4053 . . . 4
43ralbii 2888 . . 3
54anbi2i 694 . 2
61, 5bitri 249 1
 Colors of variables: wff setvar class Syntax hints:  <->wb 184  /\wa 369  =wceq 1395  e.wcel 1818  A.wral 2807  {csn 4029  Fnwfn 5588  -->wf 5589  `cfv 5593 This theorem is referenced by:  fconst3  6135  repsdf2  12750  rrxcph  21824  lnon0  25713  df0op2  26671  lfl1  34795 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-9 1822  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435  ax-sep 4573  ax-nul 4581  ax-pr 4691 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-eu 2286  df-mo 2287  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-ral 2812  df-rex 2813  df-rab 2816  df-v 3111  df-sbc 3328  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-if 3942  df-sn 4030  df-pr 4032  df-op 4036  df-uni 4250  df-br 4453  df-opab 4511  df-mpt 4512  df-id 4800  df-xp 5010  df-rel 5011  df-cnv 5012  df-co 5013  df-dm 5014  df-rn 5015  df-iota 5556  df-fun 5595  df-fn 5596  df-f 5597  df-fv 5601
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