An improved version of the semantic argument

The third premise of my semantic argument can be improved significantly. I realized this a few days ago while preparing my talk on the argument for the upcoming OZSW conference on 11 and 12 December at VU University in Amsterdam. Premise 3 of the argument can be stated as follows. If M1 and M2 are the meanings of two positive predicable generic expressions E1 and E2 such that RefSet(M1)=RefSet(M2), then M1=M2. In my paper I provide an elaborate defense of this premise. But in fact I do not need this premise. All I need for my argument to go through is the following weaker modified premise. If M1 and M2 are the meanings of two positive predicable generic expressions E1 and E2 such that RefSet(M1)=RefSet(M2), then 'x is E1 iff x is E2' is necessarily true. This modified premise is indeed weaker, since the original premise entails it but not vice versa. After all, E1 and E2 having the same meaning obviously entails that 'x is E1 iff x is E2' is necessarily true, while it is not the case that the necessary truth of 'x is E1 iff x is E2' suffices to conclude that E1 and E2 have the same meaning. Now, I suggest to replace the original premise 3 of my argument with the modified weaker premise. By doing so the conclusion of my argument, namely that there are no positive contingent universally held properties, still follows. Therefore, by doing so we have obtained a stronger version of the semantic argument, making its conclusion even more plausible.