Step |
Hyp |
Ref |
Expression |
0 |
|
cgzu |
|- AxUn |
1 |
|
c1o |
|- 1o |
2 |
|
c2o |
|- 2o |
3 |
|
cgoe |
|- e.g |
4 |
2 1 3
|
co |
|- ( 2o e.g 1o ) |
5 |
|
cgoa |
|- /\g |
6 |
|
c0 |
|- (/) |
7 |
1 6 3
|
co |
|- ( 1o e.g (/) ) |
8 |
4 7 5
|
co |
|- ( ( 2o e.g 1o ) /\g ( 1o e.g (/) ) ) |
9 |
8 1
|
cgox |
|- E.g 1o ( ( 2o e.g 1o ) /\g ( 1o e.g (/) ) ) |
10 |
|
cgoi |
|- ->g |
11 |
9 4 10
|
co |
|- ( E.g 1o ( ( 2o e.g 1o ) /\g ( 1o e.g (/) ) ) ->g ( 2o e.g 1o ) ) |
12 |
11 2
|
cgol |
|- A.g 2o ( E.g 1o ( ( 2o e.g 1o ) /\g ( 1o e.g (/) ) ) ->g ( 2o e.g 1o ) ) |
13 |
12 1
|
cgox |
|- E.g 1o A.g 2o ( E.g 1o ( ( 2o e.g 1o ) /\g ( 1o e.g (/) ) ) ->g ( 2o e.g 1o ) ) |
14 |
0 13
|
wceq |
|- AxUn = E.g 1o A.g 2o ( E.g 1o ( ( 2o e.g 1o ) /\g ( 1o e.g (/) ) ) ->g ( 2o e.g 1o ) ) |