theorem aneq2a (a b c: wff): $ (a -> (b <-> c)) -> (a /\ b <-> a /\ c) $;
| Step | Hyp | Ref | Expression |
|---|
| 1 |
|
anim2a |
(a -> b -> c) -> a /\ b -> a /\ c |
| 2 |
|
bi1 |
(b <-> c) -> b -> c |
| 3 |
2 |
imim2i |
(a -> (b <-> c)) -> a -> b -> c |
| 4 |
1, 3 |
syl |
(a -> (b <-> c)) -> a /\ b -> a /\ c |
| 5 |
|
anim2a |
(a -> c -> b) -> a /\ c -> a /\ b |
| 6 |
|
bi2 |
(b <-> c) -> c -> b |
| 7 |
6 |
imim2i |
(a -> (b <-> c)) -> a -> c -> b |
| 8 |
5, 7 |
syl |
(a -> (b <-> c)) -> a /\ c -> a /\ b |
| 9 |
4, 8 |
ibid |
(a -> (b <-> c)) -> (a /\ b <-> a /\ c) |
Axiom use
axs_prop_calc
(ax_1,
ax_2,
ax_3,
ax_mp)