Definition df-csb 2052

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 1207, to prevent ambiguity. Theorem sbcel1g 2064 shows an example of how ambiguity could arise if we didn't use distinguished brackets. Theorem sbccsbg 2073 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 2051	. 2 class [_A / x]_B
5		vy	. . . . . 6 set y
6	5	cv 991	. . . . 5 class y
7	6, 3	wcel 994	. . . 4 wff y e. B
8	7, 1, 2	wsbc 1207	. . 3 wff [A / x]y e. B
9	8, 5	cab 1505	. 2 class {y | [A / x]y e. B}
10	4, 9	wceq 992	1 wff [_A / x]_B = {y | [A / x]y e. B}

This definition is referenced by:  csbeq1 2053  cbvcsbv 2054  csbid 2056  csbcog 2058  csbexg 2059  csbconstgf 2061  sbcel12g 2062  sbceqdig 2063  csbvarg 2072  hbcsb1g 2075  hbcsbg 2077  csbiegft 2081  csbabg 2095

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