theorem bian2exi (c: wff) {x: nat} (a b: wff x):
$ a <-> b /\ c $ >
$ E. x a <-> E. x b /\ c $;
| Step | Hyp | Ref | Expression |
|---|
| 1 |
|
bitr |
(E. x a <-> E. x (b /\ c)) -> (E. x (b /\ c) <-> E. x b /\ c) -> (E. x a <-> E. x b /\ c) |
| 2 |
|
hyp h |
a <-> b /\ c |
| 3 |
2 |
exeqi |
E. x a <-> E. x (b /\ c) |
| 4 |
1, 3 |
ax_mp |
(E. x (b /\ c) <-> E. x b /\ c) -> (E. x a <-> E. x b /\ c) |
| 5 |
|
exan2 |
E. x (b /\ c) <-> E. x b /\ c |
| 6 |
4, 5 |
ax_mp |
E. x a <-> E. x b /\ c |
Axiom use
axs_prop_calc
(ax_1,
ax_2,
ax_3,
ax_mp),
axs_pred_calc
(ax_gen,
ax_4,
ax_5)