Definition df-dp2 32577

Description: Define the "decimal fraction constructor", which is used to build up "decimal fractions" in base 10. This is intentionally similar to df-dec 12700. (Contributed by David A. Wheeler, 15-May-2015.) (Revised by AV, 9-Sep-2021.)

Assertion

Ref	Expression
df-dp2	⊢ _𝐴𝐵 = (𝐴 + (𝐵 / ;10))

Detailed syntax breakdown of Definition df-dp2

Step	Hyp	Ref	Expression
1		cA	. . 3 class 𝐴
2		cB	. . 3 class 𝐵
3	1, 2	cdp2 32576	. 2 class _𝐴𝐵
4		c1 11131	. . . . 5 class 1
5		cc0 11130	. . . . 5 class 0
6	4, 5	cdc 12699	. . . 4 class ;10
7		cdiv 11893	. . . 4 class /
8	2, 6, 7	co 7414	. . 3 class (𝐵 / ;10)
9		caddc 11133	. . 3 class +
10	1, 8, 9	co 7414	. 2 class (𝐴 + (𝐵 / ;10))
11	3, 10	wceq 1534	1 wff _𝐴𝐵 = (𝐴 + (𝐵 / ;10))

This definition is referenced by:  dp2eq1  32578  dp2eq2  32579  dp20u  32583  dp20h  32584  dp2cl  32585  dp2clq  32586  rpdp2cl  32587  dp2lt10  32589  dp2lt  32590  dp2ltsuc  32591  dp2ltc  32592  dpval  32595  dpfrac1  32597  dpval2  32598  dpval3  32599  dp3mul10  32603