Definition df-nfc 2145

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 1326 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 2143	. 2 wff F/_xA
4		vy	. . . . . 6 setvar y
5	4	cv 1225	. . . . 5 class y
6	5, 2	wcel 1370	. . . 4 wff y e. A
7	6, 1	wnf 1325	. . 3 wff F/x y e. A
8	7, 4	wal 1224	. 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  2146  nfcr  2148  nfcd  2151  nfceqi  2152  nfceqdf  2155  nfnfc1  2159  nfnfc  2162  drnfc1  2172  drnfc2  2173  dfnfc2  3568