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Theorem fconst6 6256
 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 𝐵𝐶
Assertion
Ref Expression
fconst6 (𝐴 × {𝐵}):𝐴𝐶

Proof of Theorem fconst6
StepHypRef Expression
1 fconst6.1 . 2 𝐵𝐶
2 fconst6g 6255 . 2 (𝐵𝐶 → (𝐴 × {𝐵}):𝐴𝐶)
31, 2ax-mp 5 1 (𝐴 × {𝐵}):𝐴𝐶
 Colors of variables: wff setvar class Syntax hints:   ∈ wcel 2139  {csn 4321   × cxp 5264  ⟶wf 6045 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1871  ax-4 1886  ax-5 1988  ax-6 2054  ax-7 2090  ax-9 2148  ax-10 2168  ax-11 2183  ax-12 2196  ax-13 2391  ax-ext 2740  ax-sep 4933  ax-nul 4941  ax-pr 5055 This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-3an 1074  df-tru 1635  df-ex 1854  df-nf 1859  df-sb 2047  df-eu 2611  df-mo 2612  df-clab 2747  df-cleq 2753  df-clel 2756  df-nfc 2891  df-ne 2933  df-ral 3055  df-rab 3059  df-v 3342  df-dif 3718  df-un 3720  df-in 3722  df-ss 3729  df-nul 4059  df-if 4231  df-sn 4322  df-pr 4324  df-op 4328  df-br 4805  df-opab 4865  df-mpt 4882  df-id 5174  df-xp 5272  df-rel 5273  df-cnv 5274  df-co 5275  df-dm 5276  df-rn 5277  df-fun 6051  df-fn 6052  df-f 6053 This theorem is referenced by:  ramz  15951  psrlidm  19625  psrbag0  19716  00ply1bas  19832  ply1plusgfvi  19834  mbfpos  23637  i1f0  23673  axlowdimlem1  26042  axlowdimlem7  26048  axlowdim1  26059  hlim0  28422  0cnfn  29169  0lnfn  29174  circlemethnat  31049  circlevma  31050  noxp1o  32143  poimirlem29  33769  poimirlem30  33770  poimirlem31  33771  poimir  33773  broucube  33774  expgrowth  39054
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