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Definition df-ppi 25178
Description: Define the prime π function, which counts the number of primes less than or equal to 𝑥, see definition in [ApostolNT] p. 8. (Contributed by Mario Carneiro, 15-Sep-2014.)
Assertion
Ref Expression
df-ppi π = (𝑥 ∈ ℝ ↦ (♯‘((0[,]𝑥) ∩ ℙ)))

Detailed syntax breakdown of Definition df-ppi
StepHypRef Expression
1 cppi 25172 . 2 class π
2 vx . . 3 setvar 𝑥
3 cr 10223 . . 3 class
4 cc0 10224 . . . . . 6 class 0
52cv 1652 . . . . . 6 class 𝑥
6 cicc 12427 . . . . . 6 class [,]
74, 5, 6co 6878 . . . . 5 class (0[,]𝑥)
8 cprime 15719 . . . . 5 class
97, 8cin 3768 . . . 4 class ((0[,]𝑥) ∩ ℙ)
10 chash 13370 . . . 4 class
119, 10cfv 6101 . . 3 class (♯‘((0[,]𝑥) ∩ ℙ))
122, 3, 11cmpt 4922 . 2 class (𝑥 ∈ ℝ ↦ (♯‘((0[,]𝑥) ∩ ℙ)))
131, 12wceq 1653 1 wff π = (𝑥 ∈ ℝ ↦ (♯‘((0[,]𝑥) ∩ ℙ)))
Colors of variables: wff setvar class
This definition is referenced by:  ppival  25205  ppif  25208
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