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Definition df-ppi 24543
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 24537 . 2 class π
2 vx . . 3 setvar 𝑥
3 cr 9791 . . 3 class
4 cc0 9792 . . . . . 6 class 0
52cv 1473 . . . . . 6 class 𝑥
6 cicc 12005 . . . . . 6 class [,]
74, 5, 6co 6527 . . . . 5 class (0[,]𝑥)
8 cprime 15169 . . . . 5 class
97, 8cin 3538 . . . 4 class ((0[,]𝑥) ∩ ℙ)
10 chash 12934 . . . 4 class #
119, 10cfv 5790 . . 3 class (#‘((0[,]𝑥) ∩ ℙ))
122, 3, 11cmpt 4637 . 2 class (𝑥 ∈ ℝ ↦ (#‘((0[,]𝑥) ∩ ℙ)))
131, 12wceq 1474 1 wff π = (𝑥 ∈ ℝ ↦ (#‘((0[,]𝑥) ∩ ℙ)))
Colors of variables: wff setvar class
This definition is referenced by:  ppival  24570  ppif  24573
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