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Mirrors > Home > MPE Home > Th. List > axlowdimlem1 | Structured version Visualization version GIF version |
Description: Lemma for axlowdim 25641. Establish a particular constant function as a function. (Contributed by Scott Fenton, 29-Jun-2013.) |
Ref | Expression |
---|---|
axlowdimlem1 | ⊢ ((3...𝑁) × {0}):(3...𝑁)⟶ℝ |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 0re 9919 | . 2 ⊢ 0 ∈ ℝ | |
2 | 1 | fconst6 6008 | 1 ⊢ ((3...𝑁) × {0}):(3...𝑁)⟶ℝ |
Colors of variables: wff setvar class |
Syntax hints: {csn 4125 × cxp 5036 ⟶wf 5800 (class class class)co 6549 ℝcr 9814 0cc0 9815 3c3 10948 ...cfz 12197 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1713 ax-4 1728 ax-5 1827 ax-6 1875 ax-7 1922 ax-9 1986 ax-10 2006 ax-11 2021 ax-12 2034 ax-13 2234 ax-ext 2590 ax-sep 4709 ax-nul 4717 ax-pr 4833 ax-1cn 9873 ax-icn 9874 ax-addcl 9875 ax-addrcl 9876 ax-mulcl 9877 ax-mulrcl 9878 ax-i2m1 9883 ax-1ne0 9884 ax-rnegex 9886 ax-rrecex 9887 ax-cnre 9888 |
This theorem depends on definitions: df-bi 196 df-or 384 df-an 385 df-3an 1033 df-tru 1478 df-ex 1696 df-nf 1701 df-sb 1868 df-eu 2462 df-mo 2463 df-clab 2597 df-cleq 2603 df-clel 2606 df-nfc 2740 df-ne 2782 df-ral 2901 df-rex 2902 df-rab 2905 df-v 3175 df-dif 3543 df-un 3545 df-in 3547 df-ss 3554 df-nul 3875 df-if 4037 df-sn 4126 df-pr 4128 df-op 4132 df-uni 4373 df-br 4584 df-opab 4644 df-mpt 4645 df-id 4953 df-xp 5044 df-rel 5045 df-cnv 5046 df-co 5047 df-dm 5048 df-rn 5049 df-iota 5768 df-fun 5806 df-fn 5807 df-f 5808 df-fv 5812 df-ov 6552 |
This theorem is referenced by: axlowdimlem5 25626 axlowdimlem6 25627 axlowdimlem17 25638 |
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