From PhilPapers forum Logic and Philosophy of Logic:

2011-04-05
Arguments and conditionals: difference in meaning?
Reply to Gary Merrill
Hey Gary,

I was trying to explain intuitively to someone who doesn't have the background. I doubt he knows what the deduction theorem is, i.e., when and only when the turnstile can be replaced with the arrow. I noted that the issues are complex and referred him to Hunter for more on conditionals and proofs.

Cheers,

Arnold