Definition df-nfc 2573

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 1665 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

Step	Hyp	Ref	Expression
1		vx	. . 3 setvar x
2		cA	. . 3 class A
3	1, 2	wnfc 2571	. 2 wff F/_ x A
4		vy	. . . . . 6 setvar y
5	4	cv 1437	. . . . 5 class y
6	5, 2	wcel 1869	. . . 4 wff y e. A
7	6, 1	wnf 1664	. . 3 wff F/ x y e. A
8	7, 4	wal 1436	. 2 wff A. y F/ x y e. A
9	3, 8	wb 188	1 wff ( F/_ x A <-> A. y F/ x y e. A )

This definition is referenced by:  nfci  2574  nfcr  2576  nfcd  2579  nfceqdf  2580  nfceqiOLD  2582  nfnfc1  2588  nfnfc  2594  nfnfcALT  2595  drnfc1  2604  drnfc2  2605  dfnfc2  4235  nfnid  4648  bj-nfnfc  31426  bj-nfcf  31490