theorem eqtru (a: wff): $ a <-> T. <-> a $;
Step | Hyp | Ref | Expression |
1 |
|
itru |
T. |
2 |
|
id |
(a <-> T.) -> (a <-> T.) |
3 |
1, 2 |
mpbiri |
(a <-> T.) -> a |
4 |
|
id |
a -> a |
5 |
1 |
a1i |
a -> T. |
6 |
4, 5 |
bithd |
a -> (a <-> T.) |
7 |
3, 6 |
ibii |
a <-> T. <-> a |
Axiom use
axs_prop_calc
(ax_1,
ax_2,
ax_3,
ax_mp,
itru)