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Theorem fconst6 5711
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 5710 . 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 1758   {csn 3988    X. cxp 4949   -->wf 5525
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-5 1671  ax-6 1710  ax-7 1730  ax-9 1762  ax-10 1777  ax-11 1782  ax-12 1794  ax-13 1955  ax-ext 2432  ax-sep 4524  ax-nul 4532  ax-pr 4642
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 967  df-tru 1373  df-ex 1588  df-nf 1591  df-sb 1703  df-eu 2266  df-mo 2267  df-clab 2440  df-cleq 2446  df-clel 2449  df-nfc 2604  df-ne 2650  df-ral 2804  df-rex 2805  df-rab 2808  df-v 3080  df-dif 3442  df-un 3444  df-in 3446  df-ss 3453  df-nul 3749  df-if 3903  df-sn 3989  df-pr 3991  df-op 3995  df-br 4404  df-opab 4462  df-mpt 4463  df-id 4747  df-xp 4957  df-rel 4958  df-cnv 4959  df-co 4960  df-dm 4961  df-rn 4962  df-fun 5531  df-fn 5532  df-f 5533
This theorem is referenced by:  ramz  14207  psrlidm  17600  psrlidmOLD  17601  psrridmOLD  17603  psrbag0  17703  00ply1bas  17821  ply1plusgfvi  17823  mbfpos  21265  i1f0  21301  axlowdimlem1  23360  axlowdimlem7  23366  axlowdim1  23377  hlim0  24810  0cnfn  25556  0lnfn  25561  noxpsgn  27970  expgrowth  29777
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