Theorem funceq2d ≪ | index | src | ≫

theorem funceq2d (_G: wff) (F _A1 _A2 B: set):
  $ _G -> _A1 == _A2 $ >
  $ _G -> (func F _A1 B <-> func F _A2 B) $;

Step	Hyp	Ref	Expression
1		eqsidd	_G -> F == F
2		hyp _h	_G -> _A1 == _A2
3		eqsidd	_G -> B == B
4	1, 2, 3	funceqd	_G -> (func F _A1 B <-> func F _A2 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)