MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  df-nfc Structured version   Unicode version

Definition df-nfc 2593
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 1604 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  setvar  x
2 cA . . 3  class  A
31, 2wnfc 2591 . 2  wff  F/_ x A
4 vy . . . . . 6  setvar  y
54cv 1382 . . . . 5  class  y
65, 2wcel 1804 . . . 4  wff  y  e.  A
76, 1wnf 1603 . . 3  wff  F/ x  y  e.  A
87, 4wal 1381 . 2  wff  A. y F/ x  y  e.  A
93, 8wb 184 1  wff  ( F/_ x A  <->  A. y F/ x  y  e.  A )
Colors of variables: wff setvar class
This definition is referenced by:  nfci  2594  nfcr  2596  nfcd  2599  nfceqdf  2600  nfceqiOLD  2602  nfnfc1  2608  nfnfc  2614  nfnfcALT  2615  drnfc1  2624  drnfc2  2625  dfnfc2  4252  nfnid  4666  bj-nfnfc  34177  bj-nfcf  34240
  Copyright terms: Public domain W3C validator