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Mirrors > Home > MPE Home > Th. List > Mathboxes > dpval3rp | Structured version Visualization version GIF version |
Description: Value of the decimal point construct. (Contributed by Thierry Arnoux, 16-Dec-2021.) |
Ref | Expression |
---|---|
dpval3rp.a | ⊢ 𝐴 ∈ ℕ0 |
dpval3rp.b | ⊢ 𝐵 ∈ ℝ+ |
Ref | Expression |
---|---|
dpval3rp | ⊢ (𝐴.𝐵) = _𝐴𝐵 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dpval3rp.a | . 2 ⊢ 𝐴 ∈ ℕ0 | |
2 | dpval3rp.b | . . 3 ⊢ 𝐵 ∈ ℝ+ | |
3 | rpre 12748 | . . 3 ⊢ (𝐵 ∈ ℝ+ → 𝐵 ∈ ℝ) | |
4 | 2, 3 | ax-mp 5 | . 2 ⊢ 𝐵 ∈ ℝ |
5 | 1, 4 | dpval3 31176 | 1 ⊢ (𝐴.𝐵) = _𝐴𝐵 |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1539 ∈ wcel 2106 (class class class)co 7267 ℝcr 10880 ℕ0cn0 12243 ℝ+crp 12740 _cdp2 31153 .cdp 31170 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1798 ax-4 1812 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 2709 ax-sep 5221 ax-nul 5228 ax-pr 5350 |
This theorem depends on definitions: df-bi 206 df-an 397 df-or 845 df-3an 1088 df-tru 1542 df-fal 1552 df-ex 1783 df-nf 1787 df-sb 2068 df-mo 2540 df-eu 2569 df-clab 2716 df-cleq 2730 df-clel 2816 df-nfc 2889 df-ral 3069 df-rex 3070 df-rab 3073 df-v 3431 df-sbc 3716 df-dif 3889 df-un 3891 df-in 3893 df-ss 3903 df-nul 4257 df-if 4460 df-sn 4562 df-pr 4564 df-op 4568 df-uni 4840 df-br 5074 df-opab 5136 df-id 5484 df-xp 5590 df-rel 5591 df-cnv 5592 df-co 5593 df-dm 5594 df-iota 6384 df-fun 6428 df-fv 6434 df-ov 7270 df-oprab 7271 df-mpo 7272 df-rp 12741 df-dp2 31154 df-dp 31171 |
This theorem is referenced by: dp0h 31184 rpdpcl 31185 dplt 31186 dpltc 31189 dpexpp1 31190 |
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