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Theorem fconstfv 6132
 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 6055 . 2
2 fvex 5882 . . . . 5
32elsnc 4017 . . . 4
43ralbii 2854 . . 3
54anbi2i 698 . 2
61, 5bitri 252 1
 Colors of variables: wff setvar class Syntax hints:   wb 187   wa 370   wceq 1437   wcel 1867  wral 2773  csn 3993   wfn 5587  wf 5588  cfv 5592 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-5 1748  ax-6 1794  ax-7 1838  ax-9 1871  ax-10 1886  ax-11 1891  ax-12 1904  ax-13 2052  ax-ext 2398  ax-sep 4539  ax-nul 4547  ax-pr 4652 This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372  df-3an 984  df-tru 1440  df-ex 1660  df-nf 1664  df-sb 1787  df-eu 2267  df-mo 2268  df-clab 2406  df-cleq 2412  df-clel 2415  df-nfc 2570  df-ne 2618  df-ral 2778  df-rex 2779  df-rab 2782  df-v 3080  df-sbc 3297  df-dif 3436  df-un 3438  df-in 3440  df-ss 3447  df-nul 3759  df-if 3907  df-sn 3994  df-pr 3996  df-op 4000  df-uni 4214  df-br 4418  df-opab 4476  df-mpt 4477  df-id 4760  df-xp 4851  df-rel 4852  df-cnv 4853  df-co 4854  df-dm 4855  df-rn 4856  df-iota 5556  df-fun 5594  df-fn 5595  df-f 5596  df-fv 5600 This theorem is referenced by:  fconst3  6134  repsdf2  12855  rrxcph  22270  lnon0  26325  df0op2  27281  poimir  31721  lfl1  32389
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