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Mirrors > Home > ILE Home > Th. List > df-nfc | GIF version |
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 1347 for wffs; see that definition for more information. (Contributed by Mario Carneiro, 11-Aug-2016.) |
Ref | Expression |
---|---|
df-nfc | ⊢ (ℲxA ↔ ∀yℲx y ∈ A) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | vx | . . 3 setvar x | |
2 | cA | . . 3 class A | |
3 | 1, 2 | wnfc 2162 | . 2 wff ℲxA |
4 | vy | . . . . . 6 setvar y | |
5 | 4 | cv 1241 | . . . . 5 class y |
6 | 5, 2 | wcel 1390 | . . . 4 wff y ∈ A |
7 | 6, 1 | wnf 1346 | . . 3 wff Ⅎx y ∈ A |
8 | 7, 4 | wal 1240 | . 2 wff ∀yℲx y ∈ A |
9 | 3, 8 | wb 98 | 1 wff (ℲxA ↔ ∀yℲx y ∈ A) |
Colors of variables: wff set class |
This definition is referenced by: nfci 2165 nfcr 2167 nfcd 2170 nfceqi 2171 nfceqdf 2174 nfnfc1 2178 nfnfc 2181 drnfc1 2191 drnfc2 2192 dfnfc2 3589 |
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