theorem nexd (G: wff) {x: nat} (a: wff x): $ G -> ~a $ > $ G -> ~E. x a $;
| Step | Hyp | Ref | Expression |
|---|
| 1 |
|
alnex |
A. x ~a <-> ~E. x a |
| 2 |
|
hyp h |
G -> ~a |
| 3 |
2 |
iald |
G -> A. x ~a |
| 4 |
1, 3 |
sylib |
G -> ~E. x a |
Axiom use
axs_prop_calc
(ax_1,
ax_2,
ax_3,
ax_mp),
axs_pred_calc
(ax_gen,
ax_4,
ax_5)