Theorem ssel ≪ | index | src | ≫

theorem ssel (A B: set) (a: nat): $ A C_ B -> a e. A -> a e. B $;

Step	Hyp	Ref	Expression
1		eleq1	x = a -> (x e. A <-> a e. A)
2		eleq1	x = a -> (x e. B <-> a e. B)
3	1, 2	imeqd	x = a -> (x e. A -> x e. B <-> a e. A -> a e. B)
4	3	eale	A. x (x e. A -> x e. B) -> a e. A -> a e. B
5	4	conv subset	A C_ B -> a e. A -> a e. B

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)