theorem exnal {x: nat} (a: wff x): $ E. x ~a <-> ~A. x a $;
| Step | Hyp | Ref | Expression |
|---|
| 1 |
|
con2b |
(A. x a <-> ~E. x ~a) -> (E. x ~a <-> ~A. x a) |
| 2 |
|
alex |
A. x a <-> ~E. x ~a |
| 3 |
1, 2 |
ax_mp |
E. x ~a <-> ~A. x a |
Axiom use
axs_prop_calc
(ax_1,
ax_2,
ax_3,
ax_mp),
axs_pred_calc
(ax_gen,
ax_4)