Definition df-nfc 2140

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 1323 for wffs; see that definition for more information. (Contributed by Mario Carneiro, 11-Aug-2016.)

Assertion

Ref	Expression
df-nfc	|- ( F/_xA <-> 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

Step	Hyp	Ref	Expression
1		vx	. . 3 setvar x
2		cA	. . 3 class A
3	1, 2	wnfc 2138	. 2 wff F/_xA
4		vy	. . . . . 6 setvar y
5	4	cv 1222	. . . . 5 class y
6	5, 2	wcel 1366	. . . 4 wff y e. A
7	6, 1	wnf 1322	. . 3 wff F/x y e. A
8	7, 4	wal 1221	. 2 wff A.y F/x y e. A
9	3, 8	wb 98	1 wff ( F/_xA <-> A.y F/x y e. A)

This definition is referenced by:  nfci  2141  nfcr  2143  nfcd  2146  nfceqi  2147  nfceqdf  2150  nfnfc1  2154  nfnfc  2157  drnfc1  2167  drnfc2  2168  dfnfc2  3561