Theorem sseld ≪ | index | src | ≫

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

Step	Hyp	Ref	Expression
1		ssel	A C_ B -> a e. A -> a e. B
2		hyp h1	G -> A C_ B
3		hyp h2	G -> a e. A
4	1, 2, 3	sylc	G -> 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)