Metamath Proof Explorer
Description: Membership in an image of a singleton. (Contributed by NM, 15-Mar-2004) (Proof shortened by Andrew Salmon, 27-Aug-2011)
|
|
Ref |
Expression |
|
Hypotheses |
elimasn.1 |
|
|
|
elimasn.2 |
|
|
Assertion |
elimasn |
|
Proof
Step |
Hyp |
Ref |
Expression |
1 |
|
elimasn.1 |
|
2 |
|
elimasn.2 |
|
3 |
|
breq2 |
|
4 |
|
imasng |
|
5 |
1 4
|
ax-mp |
|
6 |
2 3 5
|
elab2 |
|
7 |
|
df-br |
|
8 |
6 7
|
bitri |
|