Theorem leeq1d ≪ | index | src | ≫

theorem leeq1d (_G: wff) (_a1 _a2 b: nat):
  $ _G -> _a1 = _a2 $ >
  $ _G -> (_a1 <= b <-> _a2 <= b) $;

Step	Hyp	Ref	Expression
1		hyp _h	_G -> _a1 = _a2
2		eqidd	_G -> b = b
3	1, 2	leeqd	_G -> (_a1 <= b <-> _a2 <= b)

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), axs_peano (addeq)