Theorem Ifeq1d ≪ | index | src | ≫

theorem Ifeq1d (_G _p1 _p2: wff) (A B: set):
  $ _G -> (_p1 <-> _p2) $ >
  $ _G -> If _p1 A B == If _p2 A B $;

Step	Hyp	Ref	Expression
1		hyp _h	_G -> (_p1 <-> _p2)
2		eqsidd	_G -> A == A
3		eqsidd	_G -> B == B
4	1, 2, 3	Ifeqd	_G -> If _p1 A B == If _p2 A 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)