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Mirrors > Home > MPE Home > Th. List > axlowdimlem1 | Structured version Visualization version GIF version |
Description: Lemma for axlowdim 27755. 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 11115 | . 2 ⊢ 0 ∈ ℝ | |
2 | 1 | fconst6 6729 | 1 ⊢ ((3...𝑁) × {0}):(3...𝑁)⟶ℝ |
Colors of variables: wff setvar class |
Syntax hints: {csn 4584 × cxp 5629 ⟶wf 6489 (class class class)co 7351 ℝcr 11008 0cc0 11009 3c3 12167 ...cfz 13378 |
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 1913 ax-6 1971 ax-7 2011 ax-8 2108 ax-9 2116 ax-10 2137 ax-11 2154 ax-12 2171 ax-ext 2707 ax-sep 5254 ax-nul 5261 ax-pr 5382 ax-1cn 11067 ax-addrcl 11070 ax-rnegex 11080 ax-cnre 11082 |
This theorem depends on definitions: df-bi 206 df-an 397 df-or 846 df-3an 1089 df-tru 1544 df-fal 1554 df-ex 1782 df-nf 1786 df-sb 2068 df-mo 2538 df-eu 2567 df-clab 2714 df-cleq 2728 df-clel 2814 df-nfc 2887 df-ne 2942 df-ral 3063 df-rex 3072 df-rab 3406 df-v 3445 df-dif 3911 df-un 3913 df-in 3915 df-ss 3925 df-nul 4281 df-if 4485 df-sn 4585 df-pr 4587 df-op 4591 df-br 5104 df-opab 5166 df-mpt 5187 df-id 5529 df-xp 5637 df-rel 5638 df-cnv 5639 df-co 5640 df-dm 5641 df-rn 5642 df-fun 6495 df-fn 6496 df-f 6497 |
This theorem is referenced by: axlowdimlem5 27740 axlowdimlem6 27741 axlowdimlem17 27752 |
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