Theorem Ifeq3d ≪ | index | src | ≫

theorem Ifeq3d (_G p: wff) (A _B1 _B2: set):
  $ _G -> _B1 == _B2 $ >
  $ _G -> If p A _B1 == If p A _B2 $;

Step	Hyp	Ref	Expression
1		biidd	_G -> (p <-> p)
2		eqsidd	_G -> A == A
3		hyp _h	_G -> _B1 == _B2
4	1, 2, 3	Ifeqd	_G -> If p A _B1 == If p A _B2

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)