I have following noted in my notebook:
- Transposition theorem (I hope thats what its called)
$(A\wedge B)\vee (\neg A\wedge C)=(A\vee C)\wedge(\neg A\vee B)$ - Consensus rule for transposition theorem $(A\wedge B)\vee (\neg A\wedge C)\vee (B\wedge C)=(A\wedge B)\vee(\neg A\wedge C)$
- Resolution rule
$(A\vee C)\wedge(\neg A\vee B)\rightarrow (B\vee C)$
Does this imply following?
a. From 2: $((A\wedge B)\vee(\neg A\wedge C))\rightarrow (B\wedge C)$
b. From 1 and 3: $(A\wedge B)\vee(\neg A\wedge C)\rightarrow (B\vee C)$
Its seems that these are obvious, however no book says states them explicitly. So, just confirming.