Theorem ssasymb ≪ | index | src | ≫ 

theorem ssasymb (A B: set): $ A == B <-> A C_ B /\ B C_ A $;
StepHypRefExpression
1 eqss 
A == B -> A C_ B
2 eqssr 
A == B -> B C_ A
3 1, 2 iand 
A == B -> A C_ B /\ B C_ A
4 ssasym 
A C_ B -> B C_ A -> A == B
5 4 imp 
A C_ B /\ B C_ A -> A == B
6 3, 5 ibii 
A == B <-> A C_ B /\ B C_ A

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, ax_10, ax_12), axs_set (ax_8)