Theorem fconst6 6095

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

Step	Hyp	Ref	Expression
1		fconst6.1	. 2 |- B e. C
2		fconst6g 6094	. 2 |- ( B e. C -> ( A X. { B } ) : A --> C )
3	1, 2	ax-mp 5	1 |- ( A X. { B } ) : A --> C

Syntax hints:   e. wcel 1990   {csn 4177   X. cxp 5112   -->wf 5884

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-9 1999  ax-10 2019  ax-11 2034  ax-12 2047  ax-13 2246  ax-ext 2602  ax-sep 4781  ax-nul 4789  ax-pr 4906

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-3an 1039  df-tru 1486  df-ex 1705  df-nf 1710  df-sb 1881  df-eu 2474  df-mo 2475  df-clab 2609  df-cleq 2615  df-clel 2618  df-nfc 2753  df-ne 2795  df-ral 2917  df-rab 2921  df-v 3202  df-dif 3577  df-un 3579  df-in 3581  df-ss 3588  df-nul 3916  df-if 4087  df-sn 4178  df-pr 4180  df-op 4184  df-br 4654  df-opab 4713  df-mpt 4730  df-id 5024  df-xp 5120  df-rel 5121  df-cnv 5122  df-co 5123  df-dm 5124  df-rn 5125  df-fun 5890  df-fn 5891  df-f 5892

This theorem is referenced by:  ramz  15729  psrlidm  19403  psrbag0  19494  00ply1bas  19610  ply1plusgfvi  19612  mbfpos  23418  i1f0  23454  axlowdimlem1  25822  axlowdimlem7  25828  axlowdim1  25839  hlim0  28092  0cnfn  28839  0lnfn  28844  circlemethnat  30719  circlevma  30720  noxp1o  31816  poimirlem29  33438  poimirlem30  33439  poimirlem31  33440  poimir  33442  broucube  33443  expgrowth  38534