Definition df-csb 1973

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 1153, to prevent ambiguity. Theorem sbcel1g 1984 shows an example of how ambiguity could arise if we didn't use distinguished brackets. Theorem sbccsbg 1993 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 1972	. 2 class [_A / x]_B
5		vy	. . . . . 6 set y
6	5	cv 1098	. . . . 5 class y
7	6, 3	wcel 1105	. . . 4 wff y e. B
8	7, 1, 2	wsbc 1153	. . 3 wff [A / x]y e. B
9	8, 5	cab 1440	. 2 class {y | [A / x]y e. B}
10	4, 9	wceq 1099	1 wff [_A / x]_B = {y | [A / x]y e. B}

This definition is referenced by:  csbeq1 1974  csbid 1976  csbcog 1978  csbexg 1979  csbconstgf 1981  sbcel12g 1982  sbceqdig 1983  csbvarg 1992  hbcsb1g 1995  hbcsbg 1997  csbiegft 2000  csbabg 2014  fsump1f 6900

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