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Definition df-pi 15417
Description: Define the constant pi, π = 3.14159..., which is the smallest positive number whose sine is zero. Definition of π in [Gleason] p. 311. (Contributed by Paul Chapman, 23-Jan-2008.) (Revised by AV, 14-Sep-2020.)
Assertion
Ref Expression
df-pi π = inf((ℝ+ ∩ (sin “ {0})), ℝ, < )

Detailed syntax breakdown of Definition df-pi
StepHypRef Expression
1 cpi 15411 . 2 class π
2 crp 12377 . . . 4 class +
3 csin 15408 . . . . . 6 class sin
43ccnv 5531 . . . . 5 class sin
5 cc0 10526 . . . . . 6 class 0
65csn 4539 . . . . 5 class {0}
74, 6cima 5535 . . . 4 class (sin “ {0})
82, 7cin 3907 . . 3 class (ℝ+ ∩ (sin “ {0}))
9 cr 10525 . . 3 class
10 clt 10664 . . 3 class <
118, 9, 10cinf 8893 . 2 class inf((ℝ+ ∩ (sin “ {0})), ℝ, < )
121, 11wceq 1538 1 wff π = inf((ℝ+ ∩ (sin “ {0})), ℝ, < )
Colors of variables: wff setvar class
This definition is referenced by:  pilem2  25045  pilem3  25046
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