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Theorem dpval3 30596
Description: Value of the decimal point construct. (Contributed by Thierry Arnoux, 16-Dec-2021.)
Hypotheses
Ref Expression
dpval2.a 𝐴 ∈ ℕ0
dpval2.b 𝐵 ∈ ℝ
Assertion
Ref Expression
dpval3 (𝐴.𝐵) = 𝐴𝐵

Proof of Theorem dpval3
StepHypRef Expression
1 dpval2.a . . 3 𝐴 ∈ ℕ0
2 dpval2.b . . 3 𝐵 ∈ ℝ
31, 2dpval2 30595 . 2 (𝐴.𝐵) = (𝐴 + (𝐵 / 10))
4 df-dp2 30574 . 2 𝐴𝐵 = (𝐴 + (𝐵 / 10))
53, 4eqtr4i 2824 1 (𝐴.𝐵) = 𝐴𝐵
Colors of variables: wff setvar class
Syntax hints:   = wceq 1538  wcel 2111  (class class class)co 7135  cr 10525  0cc0 10526  1c1 10527   + caddc 10529   / cdiv 11286  0cn0 11885  cdc 12086  cdp2 30573  .cdp 30590
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
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-ral 3111  df-rex 3112  df-v 3443  df-sbc 3721  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-uni 4801  df-br 5031  df-opab 5093  df-id 5425  df-xp 5525  df-rel 5526  df-cnv 5527  df-co 5528  df-dm 5529  df-iota 6283  df-fun 6326  df-fv 6332  df-ov 7138  df-oprab 7139  df-mpo 7140  df-dp2 30574  df-dp 30591
This theorem is referenced by:  dpmul100  30599  dpval3rp  30602  dp0u  30603
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