Theorem ifeq1d ≪ | index | src | ≫

theorem ifeq1d (_G _p1 _p2: wff) (a b: nat):
  $ _G -> (_p1 <-> _p2) $ >
  $ _G -> if _p1 a b = if _p2 a b $;

Step	Hyp	Ref	Expression
1		hyp _h	_G -> (_p1 <-> _p2)
2		eqidd	_G -> a = a
3		eqidd	_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), axs_the (theid, the0)