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Theorem axlowdimlem1 26241
Description: Lemma for axlowdim 26260. Establish a particular constant function as a function. (Contributed by Scott Fenton, 29-Jun-2013.)
Assertion
Ref Expression
axlowdimlem1 ((3...𝑁) × {0}):(3...𝑁)⟶ℝ

Proof of Theorem axlowdimlem1
StepHypRef Expression
1 0re 10358 . 2 0 ∈ ℝ
21fconst6 6332 1 ((3...𝑁) × {0}):(3...𝑁)⟶ℝ
Colors of variables: wff setvar class
Syntax hints:  {csn 4397   × cxp 5340  wf 6119  (class class class)co 6905  cr 10251  0cc0 10252  3c3 11407  ...cfz 12619
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1896  ax-4 1910  ax-5 2011  ax-6 2077  ax-7 2114  ax-9 2175  ax-10 2194  ax-11 2209  ax-12 2222  ax-13 2391  ax-ext 2803  ax-sep 5005  ax-nul 5013  ax-pr 5127  ax-1cn 10310  ax-addrcl 10313  ax-rnegex 10323  ax-cnre 10325
This theorem depends on definitions:  df-bi 199  df-an 387  df-or 881  df-3an 1115  df-tru 1662  df-ex 1881  df-nf 1885  df-sb 2070  df-mo 2605  df-eu 2640  df-clab 2812  df-cleq 2818  df-clel 2821  df-nfc 2958  df-ne 3000  df-ral 3122  df-rex 3123  df-rab 3126  df-v 3416  df-dif 3801  df-un 3803  df-in 3805  df-ss 3812  df-nul 4145  df-if 4307  df-sn 4398  df-pr 4400  df-op 4404  df-br 4874  df-opab 4936  df-mpt 4953  df-id 5250  df-xp 5348  df-rel 5349  df-cnv 5350  df-co 5351  df-dm 5352  df-rn 5353  df-fun 6125  df-fn 6126  df-f 6127
This theorem is referenced by:  axlowdimlem5  26245  axlowdimlem6  26246  axlowdimlem17  26257
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