theorem bian2a (a b: wff): $ (a -> b) -> (a /\ b <-> a) $;
| Step | Hyp | Ref | Expression |
|---|
| 1 |
|
anl |
a /\ b -> a |
| 2 |
1 |
a1i |
(a -> b) -> a /\ b -> a |
| 3 |
|
ian |
a -> b -> a /\ b |
| 4 |
3 |
a2i |
(a -> b) -> a -> a /\ b |
| 5 |
2, 4 |
ibid |
(a -> b) -> (a /\ b <-> a) |
Axiom use
axs_prop_calc
(ax_1,
ax_2,
ax_3,
ax_mp)