Theorem xpeqd ≪ | index | src | ≫

theorem xpeqd (_G: wff) (_A1 _A2 _B1 _B2: set):
  $ _G -> _A1 == _A2 $ >
  $ _G -> _B1 == _B2 $ >
  $ _G -> Xp _A1 _B1 == Xp _A2 _B2 $;

Step	Hyp	Ref	Expression
1		hyp _Ah	_G -> _A1 == _A2
2		hyp _Bh	_G -> _B1 == _B2
3	1, 2	xabeqd	_G -> X\ x e. _A1, _B1 == X\ x e. _A2, _B2
4	3	conv Xp	_G -> Xp _A1 _B1 == Xp _A2 _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)