Theorem ifeq2d ≪ | index | src | ≫

theorem ifeq2d (_G p: wff) (_a1 _a2 b: nat):
  $ _G -> _a1 = _a2 $ >
  $ _G -> if p _a1 b = if p _a2 b $;

Step	Hyp	Ref	Expression
1		biidd	_G -> (p <-> p)
2		hyp _h	_G -> _a1 = _a2
3		eqidd	_G -> b = b
4	1, 2, 3	ifeqd	_G -> if p _a1 b = if p _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), axs_the (theid, the0)