Mathbox for Thierry Arnoux |
< Previous
Next >
Nearby theorems |
||
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 12385 | . . 3 ⊢ (𝐵 ∈ ℝ+ → 𝐵 ∈ ℝ) | |
4 | 2, 3 | ax-mp 5 | . 2 ⊢ 𝐵 ∈ ℝ |
5 | 1, 4 | dpval3 30497 | 1 ⊢ (𝐴.𝐵) = _𝐴𝐵 |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1528 ∈ wcel 2105 (class class class)co 7145 ℝcr 10524 ℕ0cn0 11885 ℝ+crp 12377 _cdp2 30474 .cdp 30491 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1787 ax-4 1801 ax-5 1902 ax-6 1961 ax-7 2006 ax-8 2107 ax-9 2115 ax-10 2136 ax-11 2151 ax-12 2167 ax-ext 2790 ax-sep 5194 ax-nul 5201 ax-pr 5320 |
This theorem depends on definitions: df-bi 208 df-an 397 df-or 842 df-3an 1081 df-tru 1531 df-ex 1772 df-nf 1776 df-sb 2061 df-mo 2615 df-eu 2647 df-clab 2797 df-cleq 2811 df-clel 2890 df-nfc 2960 df-ral 3140 df-rex 3141 df-rab 3144 df-v 3494 df-sbc 3770 df-dif 3936 df-un 3938 df-in 3940 df-ss 3949 df-nul 4289 df-if 4464 df-sn 4558 df-pr 4560 df-op 4564 df-uni 4831 df-br 5058 df-opab 5120 df-id 5453 df-xp 5554 df-rel 5555 df-cnv 5556 df-co 5557 df-dm 5558 df-iota 6307 df-fun 6350 df-fv 6356 df-ov 7148 df-oprab 7149 df-mpo 7150 df-rp 12378 df-dp2 30475 df-dp 30492 |
This theorem is referenced by: dp0h 30505 rpdpcl 30506 dplt 30507 dpltc 30510 dpexpp1 30511 |
Copyright terms: Public domain | W3C validator |