Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > axlowdimlem1 | Structured version Visualization version GIF version |
Description: Lemma for axlowdim 26755. 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 10632 | . 2 ⊢ 0 ∈ ℝ | |
2 | 1 | fconst6 6543 | 1 ⊢ ((3...𝑁) × {0}):(3...𝑁)⟶ℝ |
Colors of variables: wff setvar class |
Syntax hints: {csn 4525 × cxp 5517 ⟶wf 6320 (class class class)co 7135 ℝcr 10525 0cc0 10526 3c3 11681 ...cfz 12885 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1797 ax-4 1811 ax-5 1911 ax-6 1970 ax-7 2015 ax-8 2113 ax-9 2121 ax-10 2142 ax-11 2158 ax-12 2175 ax-ext 2770 ax-sep 5167 ax-nul 5174 ax-pr 5295 ax-1cn 10584 ax-addrcl 10587 ax-rnegex 10597 ax-cnre 10599 |
This theorem depends on definitions: df-bi 210 df-an 400 df-or 845 df-3an 1086 df-tru 1541 df-ex 1782 df-nf 1786 df-sb 2070 df-mo 2598 df-eu 2629 df-clab 2777 df-cleq 2791 df-clel 2870 df-nfc 2938 df-ne 2988 df-ral 3111 df-rex 3112 df-v 3443 df-dif 3884 df-un 3886 df-in 3888 df-ss 3898 df-nul 4244 df-if 4426 df-sn 4526 df-pr 4528 df-op 4532 df-br 5031 df-opab 5093 df-mpt 5111 df-id 5425 df-xp 5525 df-rel 5526 df-cnv 5527 df-co 5528 df-dm 5529 df-rn 5530 df-fun 6326 df-fn 6327 df-f 6328 |
This theorem is referenced by: axlowdimlem5 26740 axlowdimlem6 26741 axlowdimlem17 26752 |
Copyright terms: Public domain | W3C validator |