Description: Two ways to express single-valuedness of a class expression A ( x ) . (Contributed by NM, 15-Oct-2010) (Proof shortened by Mario Carneiro, 18-Nov-2016)
Ref | Expression | ||
---|---|---|---|
Hypothesis | eusv2.1 | |- A e. _V |
|
Assertion | eusv2 | |- ( E! y E. x y = A <-> E! y A. x y = A ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eusv2.1 | |- A e. _V |
|
2 | 1 | eusv2nf | |- ( E! y E. x y = A <-> F/_ x A ) |
3 | eusvnfb | |- ( E! y A. x y = A <-> ( F/_ x A /\ A e. _V ) ) |
|
4 | 1 3 | mpbiran2 | |- ( E! y A. x y = A <-> F/_ x A ) |
5 | 2 4 | bitr4i | |- ( E! y E. x y = A <-> E! y A. x y = A ) |