Intuitionistic Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  ILE Home  >  Th. List  >  df-nfc Structured version   GIF version

Definition df-nfc 2149
 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 1330 for wffs; see that definition for more information. (Contributed by Mario Carneiro, 11-Aug-2016.)
Assertion
Ref Expression
df-nfc (xAyx y 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 2147 . 2 wff xA
4 vy . . . . . 6 setvar y
54cv 1227 . . . . 5 class y
65, 2wcel 1374 . . . 4 wff y A
76, 1wnf 1329 . . 3 wff x y A
87, 4wal 1226 . 2 wff yx y A
93, 8wb 98 1 wff (xAyx y A)
 Colors of variables: wff set class This definition is referenced by:  nfci  2150  nfcr  2152  nfcd  2155  nfceqi  2156  nfceqdf  2159  nfnfc1  2163  nfnfc  2166  drnfc1  2176  drnfc2  2177  dfnfc2  3572
 Copyright terms: Public domain W3C validator