MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  axlowdimlem1 Structured version   Visualization version   GIF version

Theorem axlowdimlem1 26715
Description: Lemma for axlowdim 26734. 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 10621 . 2 0 ∈ ℝ
21fconst6 6545 1 ((3...𝑁) × {0}):(3...𝑁)⟶ℝ
Colors of variables: wff setvar class
Syntax hints:  {csn 4543   × cxp 5529  wf 6327  (class class class)co 7133  cr 10514  0cc0 10515  3c3 11672  ...cfz 12876
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1911  ax-6 1970  ax-7 2015  ax-8 2116  ax-9 2124  ax-10 2145  ax-11 2161  ax-12 2177  ax-ext 2792  ax-sep 5179  ax-nul 5186  ax-pr 5306  ax-1cn 10573  ax-addrcl 10576  ax-rnegex 10586  ax-cnre 10588
This theorem depends on definitions:  df-bi 209  df-an 399  df-or 844  df-3an 1085  df-tru 1540  df-ex 1781  df-nf 1785  df-sb 2070  df-mo 2622  df-eu 2653  df-clab 2799  df-cleq 2813  df-clel 2891  df-nfc 2959  df-ne 3007  df-ral 3130  df-rex 3131  df-rab 3134  df-v 3475  df-dif 3916  df-un 3918  df-in 3920  df-ss 3930  df-nul 4270  df-if 4444  df-sn 4544  df-pr 4546  df-op 4550  df-br 5043  df-opab 5105  df-mpt 5123  df-id 5436  df-xp 5537  df-rel 5538  df-cnv 5539  df-co 5540  df-dm 5541  df-rn 5542  df-fun 6333  df-fn 6334  df-f 6335
This theorem is referenced by:  axlowdimlem5  26719  axlowdimlem6  26720  axlowdimlem17  26731
  Copyright terms: Public domain W3C validator