Definition df-pi 12008

Description: Define the constant pi, pi = 3.14159..., which is the smallest positive number whose sine is zero. Definition of pi in [Gleason] p. 311. (Contributed by Paul Chapman, 23-Jan-2008.) (Revised by AV, 14-Sep-2020.)

Assertion

Ref	Expression
df-pi	|- pi = inf ( ( RR+ i^i ( `' sin " { 0 } ) ) , RR , < )

Detailed syntax breakdown of Definition df-pi

Step	Hyp	Ref	Expression
1		cpi 12002	. 2 class pi
2		crp 9782	. . . 4 class RR+
3		csin 11999	. . . . . 6 class sin
4	3	ccnv 4678	. . . . 5 class `' sin
5		cc0 7932	. . . . . 6 class 0
6	5	csn 3634	. . . . 5 class { 0 }
7	4, 6	cima 4682	. . . 4 class ( `' sin " { 0 } )
8	2, 7	cin 3166	. . 3 class ( RR+ i^i ( `' sin " { 0 } ) )
9		cr 7931	. . 3 class RR
10		clt 8114	. . 3 class <
11	8, 9, 10	cinf 7092	. 2 class inf ( ( RR+ i^i ( `' sin " { 0 } ) ) , RR , < )
12	1, 11	wceq 1373	1 wff pi = inf ( ( RR+ i^i ( `' sin " { 0 } ) ) , RR , < )

This definition is referenced by:  pilem3  15299