theorem erexb {x: nat} (a b: wff x) (c: wff):
$ E. x (a /\ b) -> c <-> A. x (a -> b -> c) $;
| Step | Hyp | Ref | Expression |
|---|
| 1 |
|
bitr |
(E. x (a /\ b) -> c <-> A. x (a /\ b -> c)) -> (A. x (a /\ b -> c) <-> A. x (a -> b -> c)) -> (E. x (a /\ b) -> c <-> A. x (a -> b -> c)) |
| 2 |
|
eexb |
E. x (a /\ b) -> c <-> A. x (a /\ b -> c) |
| 3 |
1, 2 |
ax_mp |
(A. x (a /\ b -> c) <-> A. x (a -> b -> c)) -> (E. x (a /\ b) -> c <-> A. x (a -> b -> c)) |
| 4 |
|
impexp |
a /\ b -> c <-> a -> b -> c |
| 5 |
4 |
aleqi |
A. x (a /\ b -> c) <-> A. x (a -> b -> c) |
| 6 |
3, 5 |
ax_mp |
E. x (a /\ b) -> c <-> A. x (a -> b -> c) |
Axiom use
axs_prop_calc
(ax_1,
ax_2,
ax_3,
ax_mp,
itru),
axs_pred_calc
(ax_gen,
ax_4,
ax_5,
ax_6,
ax_7,
ax_10,
ax_12)