theorem binthd (a b c: wff): $ a -> ~b $ > $ a -> ~c $ > $ a -> (b <-> c) $;
| Step | Hyp | Ref | Expression |
|---|
| 1 |
|
con4b |
(~b <-> ~c) -> (b <-> c) |
| 2 |
|
hyp h1 |
a -> ~b |
| 3 |
|
hyp h2 |
a -> ~c |
| 4 |
2, 3 |
bithd |
a -> (~b <-> ~c) |
| 5 |
1, 4 |
syl |
a -> (b <-> c) |
Axiom use
axs_prop_calc
(ax_1,
ax_2,
ax_3,
ax_mp)