Theorem ssall ≪ | index | src | ≫ 

theorem ssall (A B: set) (l: nat): $ A C_ B -> all A l -> all B l $;
StepHypRefExpression
1 ssel 
A C_ B -> a1 e. A -> a1 e. B
2 1 imim2d 
A C_ B -> (a1 e. lmems l -> a1 e. A) -> a1 e. lmems l -> a1 e. B
3 2 alimd 
A C_ B -> A. a1 (a1 e. lmems l -> a1 e. A) -> A. a1 (a1 e. lmems l -> a1 e. B)
4 3 conv all, subset 
A C_ B -> all A l -> all B l

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)