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Definition df-gzext 30604
 Description: The Godel-set version of the Axiom of Extensionality. (Contributed by Mario Carneiro, 14-Jul-2013.)
Assertion
Ref Expression
df-gzext AxExt = (∀𝑔2𝑜((2𝑜𝑔∅) ↔𝑔 (2𝑜𝑔1𝑜)) →𝑔 (∅=𝑔1𝑜))

Detailed syntax breakdown of Definition df-gzext
StepHypRef Expression
1 cgze 30597 . 2 class AxExt
2 c2o 7441 . . . . . 6 class 2𝑜
3 c0 3874 . . . . . 6 class
4 cgoe 30569 . . . . . 6 class 𝑔
52, 3, 4co 6549 . . . . 5 class (2𝑜𝑔∅)
6 c1o 7440 . . . . . 6 class 1𝑜
72, 6, 4co 6549 . . . . 5 class (2𝑜𝑔1𝑜)
8 cgob 30586 . . . . 5 class 𝑔
95, 7, 8co 6549 . . . 4 class ((2𝑜𝑔∅) ↔𝑔 (2𝑜𝑔1𝑜))
109, 2cgol 30571 . . 3 class 𝑔2𝑜((2𝑜𝑔∅) ↔𝑔 (2𝑜𝑔1𝑜))
11 cgoq 30587 . . . 4 class =𝑔
123, 6, 11co 6549 . . 3 class (∅=𝑔1𝑜)
13 cgoi 30584 . . 3 class 𝑔
1410, 12, 13co 6549 . 2 class (∀𝑔2𝑜((2𝑜𝑔∅) ↔𝑔 (2𝑜𝑔1𝑜)) →𝑔 (∅=𝑔1𝑜))
151, 14wceq 1475 1 wff AxExt = (∀𝑔2𝑜((2𝑜𝑔∅) ↔𝑔 (2𝑜𝑔1𝑜)) →𝑔 (∅=𝑔1𝑜))
 Colors of variables: wff setvar class This definition is referenced by: (None)
 Copyright terms: Public domain W3C validator