theorem eori (a b c: wff): $ a -> c $ > $ b -> c $ > $ a \/ b -> c $;
| Step | Hyp | Ref | Expression |
|---|
| 1 |
|
hyp h1 |
a -> c |
| 2 |
1 |
a1i |
a \/ b -> a -> c |
| 3 |
|
hyp h2 |
b -> c |
| 4 |
3 |
imim2i |
(~a -> b) -> ~a -> c |
| 5 |
4 |
conv or |
a \/ b -> ~a -> c |
| 6 |
2, 5 |
casesd |
a \/ b -> c |
Axiom use
axs_prop_calc
(ax_1,
ax_2,
ax_3,
ax_mp)