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Theorem fconst6 6733
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 6732 . 2 (𝐵𝐶 → (𝐴 × {𝐵}):𝐴𝐶)
31, 2ax-mp 5 1 (𝐴 × {𝐵}):𝐴𝐶
Colors of variables: wff setvar class
Syntax hints:  wcel 2107  {csn 4587   × cxp 5632  wf 6493
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-10 2138  ax-11 2155  ax-12 2172  ax-ext 2708  ax-sep 5257  ax-nul 5264  ax-pr 5385
This theorem depends on definitions:  df-bi 206  df-an 398  df-or 847  df-3an 1090  df-tru 1545  df-fal 1555  df-ex 1783  df-nf 1787  df-sb 2069  df-mo 2539  df-eu 2568  df-clab 2715  df-cleq 2729  df-clel 2815  df-nfc 2890  df-ne 2945  df-ral 3066  df-rex 3075  df-rab 3409  df-v 3448  df-dif 3914  df-un 3916  df-in 3918  df-ss 3928  df-nul 4284  df-if 4488  df-sn 4588  df-pr 4590  df-op 4594  df-br 5107  df-opab 5169  df-mpt 5190  df-id 5532  df-xp 5640  df-rel 5641  df-cnv 5642  df-co 5643  df-dm 5644  df-rn 5645  df-fun 6499  df-fn 6500  df-f 6501
This theorem is referenced by:  ramz  16898  psrlidm  21375  psrbag0  21473  00ply1bas  21614  ply1plusgfvi  21616  mbfpos  25018  i1f0  25054  noxp1o  27014  axlowdimlem1  27894  axlowdimlem7  27900  axlowdim1  27911  hlim0  30180  0cnfn  30925  0lnfn  30930  circlemethnat  33257  circlevma  33258  poimirlem29  36110  poimirlem30  36111  poimirlem31  36112  poimir  36114  broucube  36115  expgrowth  42622
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