Theorem fsteqd ≪ | index | src | ≫

theorem fsteqd (_G: wff) (_a1 _a2: nat):
  $ _G -> _a1 = _a2 $ >
  $ _G -> fst _a1 = fst _a2 $;

Step	Hyp	Ref	Expression
1		hyp _ah	_G -> _a1 = _a2
2		eqidd	_G -> x, y = x, y
3	1, 2	eqeqd	_G -> (_a1 = x, y <-> _a2 = x, y)
4	3	exeqd	_G -> (E. y _a1 = x, y <-> E. y _a2 = x, y)
5	4	abeqd	_G -> {x \| E. y _a1 = x, y} == {x \| E. y _a2 = x, y}
6	5	theeqd	_G -> the {x \| E. y _a1 = x, y} = the {x \| E. y _a2 = x, y}
7	6	conv fst	_G -> fst _a1 = fst _a2

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)