Definition df-gzun 31353

Description: The Godel-set version of the Axiom of Unions. (Contributed by Mario Carneiro, 14-Jul-2013.)

Assertion

Ref	Expression
df-gzun	|- AxUn = E.g 1o A.g 2o ( E.g 1o ( ( 2o e.g 1o ) /\g ( 1o e.g (/) ) ) ->g ( 2o e.g 1o ) )

Detailed syntax breakdown of Definition df-gzun

Step	Hyp	Ref	Expression
1		cgzu 31346	. 2 class AxUn
2		c2o 7554	. . . . . . . 8 class 2o
3		c1o 7553	. . . . . . . 8 class 1o
4		cgoe 31315	. . . . . . . 8 class e.g
5	2, 3, 4	co 6650	. . . . . . 7 class ( 2o e.g 1o )
6		c0 3915	. . . . . . . 8 class (/)
7	3, 6, 4	co 6650	. . . . . . 7 class ( 1o e.g (/) )
8		cgoa 31329	. . . . . . 7 class /\g
9	5, 7, 8	co 6650	. . . . . 6 class ( ( 2o e.g 1o ) /\g ( 1o e.g (/) ) )
10	9, 3	cgox 31334	. . . . 5 class E.g 1o ( ( 2o e.g 1o ) /\g ( 1o e.g (/) ) )
11		cgoi 31330	. . . . 5 class ->g
12	10, 5, 11	co 6650	. . . 4 class ( E.g 1o ( ( 2o e.g 1o ) /\g ( 1o e.g (/) ) ) ->g ( 2o e.g 1o ) )
13	12, 2	cgol 31317	. . 3 class A.g 2o ( E.g 1o ( ( 2o e.g 1o ) /\g ( 1o e.g (/) ) ) ->g ( 2o e.g 1o ) )
14	13, 3	cgox 31334	. 2 class E.g 1o A.g 2o ( E.g 1o ( ( 2o e.g 1o ) /\g ( 1o e.g (/) ) ) ->g ( 2o e.g 1o ) )
15	1, 14	wceq 1483	1 wff AxUn = E.g 1o A.g 2o ( E.g 1o ( ( 2o e.g 1o ) /\g ( 1o e.g (/) ) ) ->g ( 2o e.g 1o ) )

This definition is referenced by: (None)