ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  fconst6 Unicode version

Theorem fconst6 5445
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 5444 . 2  |-  ( B  e.  C  ->  ( A  X.  { B }
) : A --> C )
31, 2ax-mp 5 1  |-  ( A  X.  { B }
) : A --> C
Colors of variables: wff set class
Syntax hints:    e. wcel 2164   {csn 3618    X. cxp 4653   -->wf 5242
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 710  ax-5 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-10 1516  ax-11 1517  ax-i12 1518  ax-bndl 1520  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546  ax-14 2167  ax-ext 2175  ax-sep 4147  ax-pow 4203  ax-pr 4238
This theorem depends on definitions:  df-bi 117  df-3an 982  df-tru 1367  df-nf 1472  df-sb 1774  df-eu 2045  df-mo 2046  df-clab 2180  df-cleq 2186  df-clel 2189  df-nfc 2325  df-ral 2477  df-rex 2478  df-v 2762  df-un 3157  df-in 3159  df-ss 3166  df-pw 3603  df-sn 3624  df-pr 3625  df-op 3627  df-br 4030  df-opab 4091  df-mpt 4092  df-id 4322  df-xp 4661  df-rel 4662  df-cnv 4663  df-co 4664  df-dm 4665  df-rn 4666  df-fun 5248  df-fn 5249  df-f 5250
This theorem is referenced by:  0ct  7156  ctm  7158  infnninfOLD  7174  exmidomni  7191  ofnegsub  8971  0nninf  15432  exmidsbthrlem  15450
  Copyright terms: Public domain W3C validator