Definition df-dp2 30124

Description: Define the "decimal fraction constructor", which is used to build up "decimal fractions" in base 10. This is intentionally similar to df-dec 11821. (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 30123	. 2 class _𝐴𝐵
4		c1 10252	. . . . 5 class 1
5		cc0 10251	. . . . 5 class 0
6	4, 5	cdc 11820	. . . 4 class ;10
7		cdiv 11008	. . . 4 class /
8	2, 6, 7	co 6904	. . 3 class (𝐵 / ;10)
9		caddc 10254	. . 3 class +
10	1, 8, 9	co 6904	. 2 class (𝐴 + (𝐵 / ;10))
11	3, 10	wceq 1658	1 wff _𝐴𝐵 = (𝐴 + (𝐵 / ;10))

This definition is referenced by:  dp2eq1  30125  dp2eq2  30126  dp20u  30130  dp20h  30131  dp2cl  30132  dp2clq  30133  rpdp2cl  30134  dp2lt10  30136  dp2lt  30137  dp2ltsuc  30138  dp2ltc  30139  dpval  30142  dpfrac1  30144  dpval2  30145  dpval3  30146  dp3mul10  30150