Theorem fstsnd ≪ | index | src | ≫

pub theorem fstsnd (a: nat): $ fst a, snd a = a $;

Step	Hyp	Ref	Expression
1		fstpr	fst (x, y) = x
2		fsteq	a = x, y -> fst a = fst (x, y)
3	1, 2	syl6eq	a = x, y -> fst a = x
4		sndpr	snd (x, y) = y
5		sndeq	a = x, y -> snd a = snd (x, y)
6	4, 5	syl6eq	a = x, y -> snd a = y
7	3, 6	preqd	a = x, y -> fst a, snd a = x, y
8		id	a = x, y -> a = x, y
9	7, 8	eqtr4d	a = x, y -> fst a, snd a = a
10	9	eex	E. y a = x, y -> fst a, snd a = a
11	10	eex	E. x E. y a = x, y -> fst a, snd a = a
12		expr	E. x E. y a = x, y
13	11, 12	ax_mp	fst a, snd a = a

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 (peano1, peano2, peano5, addeq, muleq, add0, addS, mul0, mulS)