theorem eqeq1 (a b c: nat): $ a = b -> (a = c <-> b = c) $;
| Step | Hyp | Ref | Expression |
|---|
| 1 |
|
eqtr3 |
a = b -> a = c -> b = c |
| 2 |
|
eqtr |
a = b -> b = c -> a = c |
| 3 |
1, 2 |
ibid |
a = b -> (a = c <-> b = c) |
Axiom use
axs_prop_calc
(ax_1,
ax_2,
ax_3,
ax_mp),
axs_pred_calc
(ax_gen,
ax_4,
ax_5,
ax_6,
ax_7)