Theorem eqseq1d ≪ | index | src | ≫

theorem eqseq1d (_G: wff) (_A1 _A2 B: set):
  $ _G -> _A1 == _A2 $ >
  $ _G -> (_A1 == B <-> _A2 == B) $;

Step	Hyp	Ref	Expression
1		hyp _h	_G -> _A1 == _A2
2		eqsidd	_G -> B == B
3	1, 2	eqseqd	_G -> (_A1 == B <-> _A2 == 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)