Definition df-sx

Description: Define the product sigma-algebra operation, analogous to df-tx . (Contributed by Thierry Arnoux, 1-Jun-2017)

	Ref	Expression
Assertion	df-sx	|- sX = ( s e. _V , t e. _V |-> ( sigaGen ` ran ( x e. s , y e. t |-> ( x X. y ) ) ) )

Detailed syntax breakdown

Step	Hyp	Ref	Expression
0		csx	|- sX
1		vs	|- s
2		cvv	|- _V
3		vt	|- t
4		csigagen	|- sigaGen
5		vx	|- x
6	1	cv	|- s
7		vy	|- y
8	3	cv	|- t
9	5	cv	|- x
10	7	cv	|- y
11	9 10	cxp	|- ( x X. y )
12	5 7 6 8 11	cmpo	|- ( x e. s , y e. t |-> ( x X. y ) )
13	12	crn	|- ran ( x e. s , y e. t |-> ( x X. y ) )
14	13 4	cfv	|- ( sigaGen ` ran ( x e. s , y e. t |-> ( x X. y ) ) )
15	1 3 2 2 14	cmpo	|- ( s e. _V , t e. _V |-> ( sigaGen ` ran ( x e. s , y e. t |-> ( x X. y ) ) ) )
16	0 15	wceq	|- sX = ( s e. _V , t e. _V |-> ( sigaGen ` ran ( x e. s , y e. t |-> ( x X. y ) ) ) )