Theorem oreq ≪ | index | src | ≫ 

theorem oreq (_a1 _a2 _b1 _b2: wff):
  $ (_a1 <-> _a2) -> (_b1 <-> _b2) -> (_a1 \/ _b1 <-> _a2 \/ _b2) $;
StepHypRefExpression
1 anl 
(_a1 <-> _a2) /\ (_b1 <-> _b2) -> (_a1 <-> _a2)
2 anr 
(_a1 <-> _a2) /\ (_b1 <-> _b2) -> (_b1 <-> _b2)
3 1, 2 oreqd 
(_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)