Definition df-csb 1992

Description: Define the proper substitution of a class for a set into another class. The underlined brackets distinguish it from the substitution into a wff, wsbc 1166, to prevent ambiguity. Theorem sbcel1g 2003 shows an example of how ambiguity could arise if we didn't use distinguished brackets. Theorem sbccsbg 2012 recreates substitution into a wff from this definition.

Assertion

Ref	Expression
df-csb	|- [_A / x]_B = {y | [A / x]y e. B}

Distinct variable groups:   y,A   y,B   x,y

Detailed syntax breakdown of Definition df-csb

Step	Hyp	Ref	Expression
1		vx	. . 3 set x
2		cA	. . 3 class A
3		cB	. . 3 class B
4	1, 2, 3	csb 1991	. 2 class [_A / x]_B
5		vy	. . . . . 6 set y
6	5	cv 952	. . . . 5 class y
7	6, 3	wcel 955	. . . 4 wff y e. B
8	7, 1, 2	wsbc 1166	. . 3 wff [A / x]y e. B
9	8, 5	cab 1456	. 2 class {y | [A / x]y e. B}
10	4, 9	wceq 953	1 wff [_A / x]_B = {y | [A / x]y e. B}

This definition is referenced by:  csbeq1 1993  csbid 1995  csbcog 1997  csbexg 1998  csbconstgf 2000  sbcel12g 2001  sbceqdig 2002  csbvarg 2011  hbcsb1g 2014  hbcsbg 2016  csbiegft 2019  csbabg 2033  fsump1f 6949

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