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Theorem fconst6 5781
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 5780 . 2  |-  ( B  e.  C  ->  ( A  X.  { B }
) : A --> C )
31, 2ax-mp 5 1  |-  ( A  X.  { B }
) : A --> C
Colors of variables: wff setvar class
Syntax hints:    e. wcel 1767   {csn 4033    X. cxp 5003   -->wf 5590
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-9 1771  ax-10 1786  ax-11 1791  ax-12 1803  ax-13 1968  ax-ext 2445  ax-sep 4574  ax-nul 4582  ax-pr 4692
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1382  df-ex 1597  df-nf 1600  df-sb 1712  df-eu 2279  df-mo 2280  df-clab 2453  df-cleq 2459  df-clel 2462  df-nfc 2617  df-ne 2664  df-ral 2822  df-rex 2823  df-rab 2826  df-v 3120  df-dif 3484  df-un 3486  df-in 3488  df-ss 3495  df-nul 3791  df-if 3946  df-sn 4034  df-pr 4036  df-op 4040  df-br 4454  df-opab 4512  df-mpt 4513  df-id 4801  df-xp 5011  df-rel 5012  df-cnv 5013  df-co 5014  df-dm 5015  df-rn 5016  df-fun 5596  df-fn 5597  df-f 5598
This theorem is referenced by:  ramz  14419  psrlidm  17926  psrlidmOLD  17927  psrridmOLD  17929  psrbag0  18029  00ply1bas  18151  ply1plusgfvi  18153  mbfpos  21926  i1f0  21962  axlowdimlem1  24068  axlowdimlem7  24074  axlowdim1  24085  hlim0  25976  0cnfn  26722  0lnfn  26727  noxpsgn  29352  expgrowth  31164
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