Step |
Hyp |
Ref |
Expression |
1 |
|
nnord |
|- ( A e. _om -> Ord A ) |
2 |
|
orddisj |
|- ( Ord A -> ( A i^i { A } ) = (/) ) |
3 |
1 2
|
syl |
|- ( A e. _om -> ( A i^i { A } ) = (/) ) |
4 |
|
snnzg |
|- ( A e. _om -> { A } =/= (/) ) |
5 |
|
disjpss |
|- ( ( ( A i^i { A } ) = (/) /\ { A } =/= (/) ) -> A C. ( A u. { A } ) ) |
6 |
3 4 5
|
syl2anc |
|- ( A e. _om -> A C. ( A u. { A } ) ) |
7 |
6
|
pssned |
|- ( A e. _om -> A =/= ( A u. { A } ) ) |
8 |
|
df-suc |
|- suc A = ( A u. { A } ) |
9 |
8
|
neeq2i |
|- ( A =/= suc A <-> A =/= ( A u. { A } ) ) |
10 |
7 9
|
sylibr |
|- ( A e. _om -> A =/= suc A ) |