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Theorem fconst6 6798
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 6797 . 2 (𝐵𝐶 → (𝐴 × {𝐵}):𝐴𝐶)
31, 2ax-mp 5 1 (𝐴 × {𝐵}):𝐴𝐶
Colors of variables: wff setvar class
Syntax hints:  wcel 2108  {csn 4626   × cxp 5683  wf 6557
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-10 2141  ax-11 2157  ax-12 2177  ax-ext 2708  ax-sep 5296  ax-nul 5306  ax-pr 5432
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 849  df-3an 1089  df-tru 1543  df-fal 1553  df-ex 1780  df-nf 1784  df-sb 2065  df-mo 2540  df-eu 2569  df-clab 2715  df-cleq 2729  df-clel 2816  df-nfc 2892  df-ne 2941  df-ral 3062  df-rex 3071  df-rab 3437  df-v 3482  df-dif 3954  df-un 3956  df-ss 3968  df-nul 4334  df-if 4526  df-sn 4627  df-pr 4629  df-op 4633  df-br 5144  df-opab 5206  df-mpt 5226  df-id 5578  df-xp 5691  df-rel 5692  df-cnv 5693  df-co 5694  df-dm 5695  df-rn 5696  df-fun 6563  df-fn 6564  df-f 6565
This theorem is referenced by:  ramz  17063  psrlidm  21982  psrbag0  22086  00ply1bas  22241  ply1plusgfvi  22243  mbfpos  25686  i1f0  25722  noxp1o  27708  axlowdimlem1  28957  axlowdimlem7  28963  axlowdim1  28974  hlim0  31254  0cnfn  31999  0lnfn  32004  elrgspnlem1  33246  circlemethnat  34656  circlevma  34657  poimirlem29  37656  poimirlem30  37657  poimirlem31  37658  poimir  37660  broucube  37661  expgrowth  44354
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