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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
StepHypRef Expression
1 vx . . 3 set x
2 cA . . 3 class A
3 cB . . 3 class B
41, 2, 3csb 1991 . 2 class [_A / x]_B
5 vy . . . . . 6 set y
65cv 952 . . . . 5 class y
76, 3wcel 955 . . . 4 wff y e. B
87, 1, 2wsbc 1166 . . 3 wff [A / x]y e. B
98, 5cab 1456 . 2 class {y | [A / x]y e. B}
104, 9wceq 953 1 wff [_A / x]_B = {y | [A / x]y e. B}
Colors of variables: wff set class
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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