Description: An element not in a set can be removed without affecting the set. (Contributed by NM, 16-Mar-2006) (Proof shortened by Andrew Salmon, 29-Jun-2011)
Ref | Expression | ||
---|---|---|---|
Assertion | difsn | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eldifsn | |
|
2 | simpl | |
|
3 | nelelne | |
|
4 | 3 | ancld | |
5 | 2 4 | impbid2 | |
6 | 1 5 | bitrid | |
7 | 6 | eqrdv | |