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Definition df-inn 7696
Description: Definition of the set of positive integers. For naming consistency with the Metamath Proof Explorer usages should refer to dfnn2 7697 instead. (Contributed by Jeff Hankins, 12-Sep-2013.) (Revised by Mario Carneiro, 3-May-2014.) (New usage is discouraged.)
Assertion
Ref Expression
df-inn ℕ = {x ∣ (1 x y x (y + 1) x)}
Distinct variable group:   x,y

Detailed syntax breakdown of Definition df-inn
StepHypRef Expression
1 cn 7695 . 2 class
2 c1 6712 . . . . . 6 class 1
3 vx . . . . . . 7 setvar x
43cv 1241 . . . . . 6 class x
52, 4wcel 1390 . . . . 5 wff 1 x
6 vy . . . . . . . . 9 setvar y
76cv 1241 . . . . . . . 8 class y
8 caddc 6714 . . . . . . . 8 class +
97, 2, 8co 5455 . . . . . . 7 class (y + 1)
109, 4wcel 1390 . . . . . 6 wff (y + 1) x
1110, 6, 4wral 2300 . . . . 5 wff y x (y + 1) x
125, 11wa 97 . . . 4 wff (1 x y x (y + 1) x)
1312, 3cab 2023 . . 3 class {x ∣ (1 x y x (y + 1) x)}
1413cint 3606 . 2 class {x ∣ (1 x y x (y + 1) x)}
151, 14wceq 1242 1 wff ℕ = {x ∣ (1 x y x (y + 1) x)}
Colors of variables: wff set class
This definition is referenced by:  dfnn2  7697
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