theorem con3b (a b: wff): $ (a <-> b) -> (~a <-> ~b) $;
| Step | Hyp | Ref | Expression |
|---|
| 1 |
|
bi2 |
(a <-> b) -> b -> a |
| 2 |
1 |
con3d |
(a <-> b) -> ~a -> ~b |
| 3 |
|
bi1 |
(a <-> b) -> a -> b |
| 4 |
3 |
con3d |
(a <-> b) -> ~b -> ~a |
| 5 |
2, 4 |
ibid |
(a <-> b) -> (~a <-> ~b) |
Axiom use
axs_prop_calc
(ax_1,
ax_2,
ax_3,
ax_mp)