Theorem Sndss ≪ | index | src | ≫

theorem Sndss (A B: set): $ A C_ B -> Snd A C_ Snd B $;

Step	Hyp	Ref	Expression
1		ssel	A C_ B -> b1 a1 e. A -> b1 a1 e. B
2	1	ssabd	A C_ B -> {a1 \| b1 a1 e. A} C_ {a1 \| b1 a1 e. B}
3	2	conv Snd	A C_ B -> Snd A C_ Snd B

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)