Theorem inseq ≪ | index | src | ≫

theorem inseq (_a1 _a2 _b1 _b2: nat):
  $ _a1 = _a2 -> _b1 = _b2 -> _a1 ; _b1 = _a2 ; _b2 $;

Step	Hyp	Ref	Expression
1		anl	_a1 = _a2 /\ _b1 = _b2 -> _a1 = _a2
2		anr	_a1 = _a2 /\ _b1 = _b2 -> _b1 = _b2
3	1, 2	inseqd	_a1 = _a2 /\ _b1 = _b2 -> _a1 ; _b1 = _a2 ; _b2
4	3	exp	_a1 = _a2 -> _b1 = _b2 -> _a1 ; _b1 = _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), axs_the (theid, the0), axs_peano (peano2, addeq, muleq)