theorem rexral {x y: nat} (a: wff x) (b: wff y) (c: wff x y):
$ E. x (a /\ A. y (b -> c)) -> A. y (b -> E. x (a /\ c)) $;
| Step | Hyp | Ref | Expression |
|---|
| 1 |
|
exral |
E. x A. y (b -> a /\ c) -> A. y (b -> E. x (a /\ c)) |
| 2 |
|
alan1 |
A. y (a /\ (b -> c)) <-> a /\ A. y (b -> c) |
| 3 |
|
imancom |
a /\ (b -> c) -> b -> a /\ c |
| 4 |
3 |
alimi |
A. y (a /\ (b -> c)) -> A. y (b -> a /\ c) |
| 5 |
2, 4 |
sylbir |
a /\ A. y (b -> c) -> A. y (b -> a /\ c) |
| 6 |
5 |
eximi |
E. x (a /\ A. y (b -> c)) -> E. x A. y (b -> a /\ c) |
| 7 |
1, 6 |
syl |
E. x (a /\ A. y (b -> c)) -> A. y (b -> E. x (a /\ c)) |
Axiom use
axs_prop_calc
(ax_1,
ax_2,
ax_3,
ax_mp),
axs_pred_calc
(ax_gen,
ax_4,
ax_5,
ax_6,
ax_7,
ax_10,
ax_11,
ax_12)