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Definition df-nfc 2381
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 "for all" or something that expands to one (such as "there exists"). It is defined in terms of the not-free predicate df-nf 1540 for wffs; see that definition for more information. (Contributed by Mario Carneiro, 11-Aug-2016.)
Assertion
Ref Expression
df-nfc  |-  ( F/_ x A  <->  A. y F/ x  y  e.  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  set  x
2 cA . . 3  class  A
31, 2wnfc 2379 . 2  wff  F/_ x A
4 vy . . . . . 6  set  y
54cv 1618 . . . . 5  class  y
65, 2wcel 1621 . . . 4  wff  y  e.  A
76, 1wnf 1539 . . 3  wff  F/ x  y  e.  A
87, 4wal 1532 . 2  wff  A. y F/ x  y  e.  A
93, 8wb 178 1  wff  ( F/_ x A  <->  A. y F/ x  y  e.  A )
Colors of variables: wff set class
This definition is referenced by:  nfci  2382  nfcr  2384  nfcd  2387  nfceqi  2388  nfceqdf  2391  nfnfc1  2395  nfnfc  2398  drnfc1  2408  drnfc2  2409  dfnfc2  3805  nfnid  4162
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