Yes; putting essentially the same example another way, we might feel intuitively that there are two separate proofs of the propositional theorem that "B AND C"

Yes; putting essentially the same example another way, we might feel intuitively that there are two separate proofs of the propositional theorem that "B AND C" implies "B OR C". Edit: Or, following up on danharaj's framing, we might feel intuitively that there are two separate proofs of "The set {B, C} is inhabited".