![]() |
Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > MPE Home > Th. List > axlowdimlem1 | Structured version Visualization version GIF version |
Description: Lemma for axlowdim 26260. 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 10358 | . 2 ⊢ 0 ∈ ℝ | |
2 | 1 | fconst6 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 ℝcr 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 |
Copyright terms: Public domain | W3C validator |