theorem ralim1 {x: nat} (a: wff) (p b: wff x):
$ A. x (p -> a -> b) <-> a -> A. x (p -> b) $;
| Step | Hyp | Ref | Expression |
|---|
| 1 |
|
bitr |
(A. x (p -> a -> b) <-> A. x (a -> p -> b)) -> (A. x (a -> p -> b) <-> a -> A. x (p -> b)) -> (A. x (p -> a -> b) <-> a -> A. x (p -> b)) |
| 2 |
|
com12b |
p -> a -> b <-> a -> p -> b |
| 3 |
2 |
aleqi |
A. x (p -> a -> b) <-> A. x (a -> p -> b) |
| 4 |
1, 3 |
ax_mp |
(A. x (a -> p -> b) <-> a -> A. x (p -> b)) -> (A. x (p -> a -> b) <-> a -> A. x (p -> b)) |
| 5 |
|
alim1 |
A. x (a -> p -> b) <-> a -> A. x (p -> b) |
| 6 |
4, 5 |
ax_mp |
A. x (p -> a -> b) <-> a -> A. x (p -> b) |
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)