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Definition df-nfc 2164
Description: Define the not-free predicate for classes. This is read "x is not free in A". Not-free means that the value of x cannot affect the value of A, e.g., any occurrence of x in A is effectively bound by a quantifier or something that expands to one (such as "there exists at most one"). It is defined in terms of the not-free predicate df-nf 1347 for wffs; see that definition for more information. (Contributed by Mario Carneiro, 11-Aug-2016.)
Assertion
Ref Expression
df-nfc (xAyx y A)
Distinct variable groups:   x,y   y,A
Allowed substitution hint:   A(x)

Detailed syntax breakdown of Definition df-nfc
StepHypRef Expression
1 vx . . 3 setvar x
2 cA . . 3 class A
31, 2wnfc 2162 . 2 wff xA
4 vy . . . . . 6 setvar y
54cv 1241 . . . . 5 class y
65, 2wcel 1390 . . . 4 wff y A
76, 1wnf 1346 . . 3 wff x y A
87, 4wal 1240 . 2 wff yx y A
93, 8wb 98 1 wff (xAyx y A)
Colors of variables: wff set class
This definition is referenced by:  nfci  2165  nfcr  2167  nfcd  2170  nfceqi  2171  nfceqdf  2174  nfnfc1  2178  nfnfc  2181  drnfc1  2191  drnfc2  2192  dfnfc2  3589
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