> Just because X implies Y does not mean ~Y implies ~X.
As others have mentioned, X implies Y does in fact require ~Y implies ~X. I think your example is confusing because "the government is corrupt" means many different things, but you're using it in a rather specific way ("the government is protecting SBF"). The equivalence of `X implies Y` and `~Y implies ~X` is more manifest through the following example
"The government is protecting SBF, so SBF won't go to jail"
and
"SBF went to jail, so the government wasn't protecting him."
As others have mentioned, X implies Y does in fact require ~Y implies ~X. I think your example is confusing because "the government is corrupt" means many different things, but you're using it in a rather specific way ("the government is protecting SBF"). The equivalence of `X implies Y` and `~Y implies ~X` is more manifest through the following example
and