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Theorem fconst6 5431
Description: A constant function as a mapping. (Contributed by Jeff Madsen, 30-Nov-2009.) (Revised by Mario Carneiro, 22-Apr-2015.)
Hypothesis
Ref Expression
fconst6.1  |-  B  e.  C
Assertion
Ref Expression
fconst6  |-  ( A  X.  { B }
) : A --> C

Proof of Theorem fconst6
StepHypRef Expression
1 fconst6.1 . 2  |-  B  e.  C
2 fconst6g 5430 . 2  |-  ( B  e.  C  ->  ( A  X.  { B }
) : A --> C )
31, 2ax-mp 8 1  |-  ( A  X.  { B }
) : A --> C
Colors of variables: wff set class
Syntax hints:    e. wcel 1684   {csn 3640    X. cxp 4687   -->wf 5251
This theorem is referenced by:  ramz  13072  psrlidm  16148  psrridm  16149  psrbag0  16235  00ply1bas  16318  ply1plusgfvi  16320  mbfpos  19006  i1f0  19042  mdeg0  19456  hlim0  21815  0cnfn  22560  0lnfn  22565  noxpsgn  24319  axlowdimlem1  24570  axlowdimlem7  24576  axlowdim1  24587  expgrowth  27552
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 1635  ax-8 1643  ax-14 1688  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264  ax-sep 4141  ax-nul 4149  ax-pr 4214
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 1630  df-eu 2147  df-mo 2148  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-ne 2448  df-ral 2548  df-rex 2549  df-rab 2552  df-v 2790  df-dif 3155  df-un 3157  df-in 3159  df-ss 3166  df-nul 3456  df-if 3566  df-sn 3646  df-pr 3647  df-op 3649  df-br 4024  df-opab 4078  df-mpt 4079  df-id 4309  df-xp 4695  df-rel 4696  df-cnv 4697  df-co 4698  df-dm 4699  df-rn 4700  df-fun 5257  df-fn 5258  df-f 5259
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