Description: The prime-counting function ppi at 2 . (Contributed by Mario Carneiro, 21-Sep-2014)
Ref | Expression | ||
---|---|---|---|
Assertion | ppi2 | ⊢ ( π ‘ 2 ) = 1 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 1nn0 | ⊢ 1 ∈ ℕ0 | |
2 | df-2 | ⊢ 2 = ( 1 + 1 ) | |
3 | ppi1 | ⊢ ( π ‘ 1 ) = 0 | |
4 | 2prm | ⊢ 2 ∈ ℙ | |
5 | 1 2 3 4 | ppi1i | ⊢ ( π ‘ 2 ) = ( 0 + 1 ) |
6 | 1e0p1 | ⊢ 1 = ( 0 + 1 ) | |
7 | 5 6 | eqtr4i | ⊢ ( π ‘ 2 ) = 1 |