Theorem cardeqd ≪ | index | src | ≫

theorem cardeqd (_G: wff) (_s1 _s2: nat):
  $ _G -> _s1 = _s2 $ >
  $ _G -> card _s1 = card _s2 $;

Step	Hyp	Ref	Expression
1		eqsidd	_G -> \ f, f @ (size (Dom f) // 2) + size (Dom f) % 2 == \ f, f @ (size (Dom f) // 2) + size (Dom f) % 2
2		hyp _sh	_G -> _s1 = _s2
3	1, 2	sreceqd	_G -> srec (\ f, f @ (size (Dom f) // 2) + size (Dom f) % 2) _s1 = srec (\ f, f @ (size (Dom f) // 2) + size (Dom f) % 2) _s2
4	3	conv card	_G -> card _s1 = card _s2

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), axs_peano (peano2, addeq, muleq)