Theorem ssv1 ≪ | index | src | ≫

theorem ssv1 (A: set): $ _V C_ A <-> A == _V $;

Step	Hyp	Ref	Expression
1		ssasym	A C_ _V -> _V C_ A -> A == _V
2		ssv2	A C_ _V
3	1, 2	ax_mp	_V C_ A -> A == _V
4		ssid	_V C_ _V
5		sseq2	A == _V -> (_V C_ A <-> _V C_ _V)
6	4, 5	mpbiri	A == _V -> _V C_ A
7	3, 6	ibii	_V C_ A <-> A == _V

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)