Theorem neeq ≪ | index | src | ≫

theorem neeq (_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	neeqd	_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), axs_pred_calc (ax_gen, ax_4, ax_5, ax_6, ax_7)