Theorem oreqd ≪ | index | src | ≫

theorem oreqd (_G _a1 _a2 _b1 _b2: wff):
  $ _G -> (_a1 <-> _a2) $ >
  $ _G -> (_b1 <-> _b2) $ >
  $ _G -> (_a1 \/ _b1 <-> _a2 \/ _b2) $;

Step	Hyp	Ref	Expression
1		hyp _ah	_G -> (_a1 <-> _a2)
2	1	noteqd	_G -> (~_a1 <-> ~_a2)
3		hyp _bh	_G -> (_b1 <-> _b2)
4	2, 3	imeqd	_G -> (~_a1 -> _b1 <-> ~_a2 -> _b2)
5	4	conv or	_G -> (_a1 \/ _b1 <-> _a2 \/ _b2)

Axiom use

axs_prop_calc (ax_1, ax_2, ax_3, ax_mp)