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Mirrors > Home > MPE Home > Th. List > Mathboxes > dpval3 | Structured version Visualization version GIF version |
Description: Value of the decimal point construct. (Contributed by Thierry Arnoux, 16-Dec-2021.) |
Ref | Expression |
---|---|
dpval2.a | ⊢ 𝐴 ∈ ℕ0 |
dpval2.b | ⊢ 𝐵 ∈ ℝ |
Ref | Expression |
---|---|
dpval3 | ⊢ (𝐴.𝐵) = _𝐴𝐵 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dpval2.a | . . 3 ⊢ 𝐴 ∈ ℕ0 | |
2 | dpval2.b | . . 3 ⊢ 𝐵 ∈ ℝ | |
3 | 1, 2 | dpval2 29601 | . 2 ⊢ (𝐴.𝐵) = (𝐴 + (𝐵 / ;10)) |
4 | df-dp2 29578 | . 2 ⊢ _𝐴𝐵 = (𝐴 + (𝐵 / ;10)) | |
5 | 3, 4 | eqtr4i 2647 | 1 ⊢ (𝐴.𝐵) = _𝐴𝐵 |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1483 ∈ wcel 1990 (class class class)co 6650 ℝcr 9935 0cc0 9936 1c1 9937 + caddc 9939 / cdiv 10684 ℕ0cn0 11292 ;cdc 11493 _cdp2 29577 .cdp 29595 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 ax-sep 4781 ax-nul 4789 ax-pr 4906 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-3an 1039 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-eu 2474 df-mo 2475 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-ral 2917 df-rex 2918 df-rab 2921 df-v 3202 df-sbc 3436 df-dif 3577 df-un 3579 df-in 3581 df-ss 3588 df-nul 3916 df-if 4087 df-sn 4178 df-pr 4180 df-op 4184 df-uni 4437 df-br 4654 df-opab 4713 df-id 5024 df-xp 5120 df-rel 5121 df-cnv 5122 df-co 5123 df-dm 5124 df-iota 5851 df-fun 5890 df-fv 5896 df-ov 6653 df-oprab 6654 df-mpt2 6655 df-dp2 29578 df-dp 29596 |
This theorem is referenced by: dpmul100 29605 dpval3rp 29608 dp0u 29609 |
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