Theorem Ifeq2d ≪ | index | src | ≫

theorem Ifeq2d (_G p: wff) (_A1 _A2 B: set):
  $ _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		eqsidd	_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)