Theorem ifeq3d ≪ | index | src | ≫

theorem ifeq3d (_G p: wff) (a _b1 _b2: nat):
  $ _G -> _b1 = _b2 $ >
  $ _G -> if p a _b1 = if p a _b2 $;

Step	Hyp	Ref	Expression
1		biidd	_G -> (p <-> p)
2		eqidd	_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), axs_the (theid, the0)