MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  fconst6 Structured version   Unicode version

Theorem fconst6 5633
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 5632 . 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 1725   {csn 3814    X. cxp 4876   -->wf 5450
This theorem is referenced by:  ramz  13393  psrlidm  16467  psrridm  16468  psrbag0  16554  00ply1bas  16634  ply1plusgfvi  16636  mbfpos  19543  i1f0  19579  mdeg0  19993  hlim0  22738  0cnfn  23483  0lnfn  23488  noxpsgn  25620  axlowdimlem1  25881  axlowdimlem7  25887  axlowdim1  25898  expgrowth  27529
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417  ax-sep 4330  ax-nul 4338  ax-pr 4403
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-eu 2285  df-mo 2286  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ne 2601  df-ral 2710  df-rex 2711  df-rab 2714  df-v 2958  df-dif 3323  df-un 3325  df-in 3327  df-ss 3334  df-nul 3629  df-if 3740  df-sn 3820  df-pr 3821  df-op 3823  df-br 4213  df-opab 4267  df-mpt 4268  df-id 4498  df-xp 4884  df-rel 4885  df-cnv 4886  df-co 4887  df-dm 4888  df-rn 4889  df-fun 5456  df-fn 5457  df-f 5458
  Copyright terms: Public domain W3C validator