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Definition df-nfc 2739
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 1700 for wffs; see that definition for more information. (Contributed by Mario Carneiro, 11-Aug-2016.)
Assertion
Ref Expression
df-nfc (𝑥𝐴 ↔ ∀𝑦𝑥 𝑦𝐴)
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 2737 . 2 wff 𝑥𝐴
4 vy . . . . . 6 setvar 𝑦
54cv 1473 . . . . 5 class 𝑦
65, 2wcel 1976 . . . 4 wff 𝑦𝐴
76, 1wnf 1698 . . 3 wff 𝑥 𝑦𝐴
87, 4wal 1472 . 2 wff 𝑦𝑥 𝑦𝐴
93, 8wb 194 1 wff (𝑥𝐴 ↔ ∀𝑦𝑥 𝑦𝐴)
Colors of variables: wff setvar class
This definition is referenced by:  nfci  2740  nfcr  2742  nfcd  2745  nfceqdf  2746  nfnfc1  2753  nfnfc  2759  nfnfcALT  2760  drnfc1  2767  drnfc2  2768  dfnfc2  4384  dfnfc2OLD  4385  nfnid  4817  bj-nfnfc  31830  bj-nfcf  31895
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