[FOM] The Irrelevance of definite descriptions in the Slingshot Argument?

[Neil Tennant]

How does (3) follow from (2) in either of these arguments?
Neil Tennant

On Thu, 28 Sep 2006 A.S.Virdi at lse.ac.uk wrote:

> Can anyone think of any significant mathematical difference between the
> following two arguments? 
> 
> 1. s                                                    Premise
> 2. {x: x = d & s} = {x: x = d}  From 1., given substitution salva
> veritate of logical equivalents
> 3. {x: x = d & t} = {x: x = d}  From 2., given substitution salva
> veritate of co-referring terms
> 4. t                            From 3., given substitution salva
> veritate of logical equivalents
> 
> And (with i is the iota/definite-description operator)
> 
> 1. s                                                    Premise
> 2. ix(x = d & s) = ix(x = d)    From 1., given substitution salva
> veritate of logical equivalents 
> 3. ix(x = d & t) = ix(x = d)    From 2., given substitution salva
> veritate of co-referring terms
> 4. t                            From 3., given substitution salva
> veritate of logical equivalents