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Definition df-ppi 25604
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 25598 . 2 class π
2 vx . . 3 setvar 𝑥
3 cr 10524 . . 3 class
4 cc0 10525 . . . . . 6 class 0
52cv 1527 . . . . . 6 class 𝑥
6 cicc 12729 . . . . . 6 class [,]
74, 5, 6co 7145 . . . . 5 class (0[,]𝑥)
8 cprime 16003 . . . . 5 class
97, 8cin 3932 . . . 4 class ((0[,]𝑥) ∩ ℙ)
10 chash 13678 . . . 4 class
119, 10cfv 6348 . . 3 class (♯‘((0[,]𝑥) ∩ ℙ))
122, 3, 11cmpt 5137 . 2 class (𝑥 ∈ ℝ ↦ (♯‘((0[,]𝑥) ∩ ℙ)))
131, 12wceq 1528 1 wff π = (𝑥 ∈ ℝ ↦ (♯‘((0[,]𝑥) ∩ ℙ)))
Colors of variables: wff setvar class
This definition is referenced by:  ppival  25631  ppif  25634
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