Theorem ssin2 ≪ | index | src | ≫ 

theorem ssin2 (A B C: set): $ B C_ C -> A i^i B C_ A i^i C $;
StepHypRefExpression
1 ssin 
A i^i B C_ A i^i C <-> A i^i B C_ A /\ A i^i B C_ C
2 inss1 
A i^i B C_ A
3 2 a1i 
B C_ C -> A i^i B C_ A
4 sstr 
A i^i B C_ B -> B C_ C -> A i^i B C_ C
5 inss2 
A i^i B C_ B
6 4, 5 ax_mp 
B C_ C -> A i^i B C_ C
7 3, 6 iand 
B C_ C -> A i^i B C_ A /\ A i^i B C_ C
8 1, 7 sylibr 
B C_ C -> A i^i B C_ A i^i C

Axiom use

axs_prop_calc (ax_1, ax_2, ax_3, ax_mp, itru), axs_pred_calc (ax_gen, ax_4, ax_5, ax_6, ax_7, ax_10, ax_11, ax_12), axs_set (elab, ax_8)