theorem exeq {x: nat} (a b: wff x): $ A. x (a <-> b) -> (E. x a <-> E. x b) $;
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | aleq | A. x (~a <-> ~b) -> (A. x ~a <-> A. x ~b) |
|
| 2 | noteq | (a <-> b) -> (~a <-> ~b) |
|
| 3 | 2 | alimi | A. x (a <-> b) -> A. x (~a <-> ~b) |
| 4 | 1, 3 | syl | A. x (a <-> b) -> (A. x ~a <-> A. x ~b) |
| 5 | 4 | noteqd | A. x (a <-> b) -> (~A. x ~a <-> ~A. x ~b) |
| 6 | 5 | conv ex | A. x (a <-> b) -> (E. x a <-> E. x b) |