theorem birexan2i (a: wff) {x: nat} (p b c: wff x):
  $ b <-> E. x (p /\ c) $ >
  $ a /\ b <-> E. x (p /\ (a /\ c)) $;
    | Step | Hyp | Ref | Expression | 
|---|---|---|---|
| 1 | hyp h | b <-> E. x (p /\ c) | |
| 2 | 1 | a1i | a -> (b <-> E. x (p /\ c)) | 
| 3 | 2 | birexan2a | a /\ b <-> E. x (p /\ (a /\ c)) |