Theorem ssin1 ≪ | index | src | ≫ 

theorem ssin1 (A B C: set): $ A C_ B -> A i^i C C_ B i^i C $;
StepHypRefExpression
1 ssin 
A i^i C C_ B i^i C <-> A i^i C C_ B /\ A i^i C C_ C
2 sstr 
A i^i C C_ A -> A C_ B -> A i^i C C_ B
3 inss1 
A i^i C C_ A
4 2, 3 ax_mp 
A C_ B -> A i^i C C_ B
5 inss2 
A i^i C C_ C
6 5 a1i 
A C_ B -> A i^i C C_ C
7 4, 6 iand 
A C_ B -> A i^i C C_ B /\ A i^i C C_ C
8 1, 7 sylibr 
A C_ B -> A i^i C C_ B 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)