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Definition df-gzinf 32762
Description: The Godel-set version of the Axiom of Infinity. (Contributed by Mario Carneiro, 14-Jul-2013.)
Assertion
Ref Expression
df-gzinf AxInf = ∃𝑔1o((∅∈𝑔1o)∧𝑔𝑔2o((2o𝑔1o) →𝑔𝑔∅((2o𝑔∅)∧𝑔(∅∈𝑔1o))))

Detailed syntax breakdown of Definition df-gzinf
StepHypRef Expression
1 cgzi 32755 . 2 class AxInf
2 c0 4276 . . . . 5 class
3 c1o 8091 . . . . 5 class 1o
4 cgoe 32637 . . . . 5 class 𝑔
52, 3, 4co 7149 . . . 4 class (∅∈𝑔1o)
6 c2o 8092 . . . . . . 7 class 2o
76, 3, 4co 7149 . . . . . 6 class (2o𝑔1o)
86, 2, 4co 7149 . . . . . . . 8 class (2o𝑔∅)
9 cgoa 32737 . . . . . . . 8 class 𝑔
108, 5, 9co 7149 . . . . . . 7 class ((2o𝑔∅)∧𝑔(∅∈𝑔1o))
1110, 2cgox 32742 . . . . . 6 class 𝑔∅((2o𝑔∅)∧𝑔(∅∈𝑔1o))
12 cgoi 32738 . . . . . 6 class 𝑔
137, 11, 12co 7149 . . . . 5 class ((2o𝑔1o) →𝑔𝑔∅((2o𝑔∅)∧𝑔(∅∈𝑔1o)))
1413, 6cgol 32639 . . . 4 class 𝑔2o((2o𝑔1o) →𝑔𝑔∅((2o𝑔∅)∧𝑔(∅∈𝑔1o)))
155, 14, 9co 7149 . . 3 class ((∅∈𝑔1o)∧𝑔𝑔2o((2o𝑔1o) →𝑔𝑔∅((2o𝑔∅)∧𝑔(∅∈𝑔1o))))
1615, 3cgox 32742 . 2 class 𝑔1o((∅∈𝑔1o)∧𝑔𝑔2o((2o𝑔1o) →𝑔𝑔∅((2o𝑔∅)∧𝑔(∅∈𝑔1o))))
171, 16wceq 1538 1 wff AxInf = ∃𝑔1o((∅∈𝑔1o)∧𝑔𝑔2o((2o𝑔1o) →𝑔𝑔∅((2o𝑔∅)∧𝑔(∅∈𝑔1o))))
Colors of variables: wff setvar class
This definition is referenced by: (None)
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