The question was:

Lc = {<G> : G is a context-free grammar and L(G) is in C}

is it true that for all C - a non trivial property of CFLs Lc is not in R?

The answer was no, C = {PHI}

I understand why this is true, but

say I was trying to prove the claim true, I would have built a reduction from Atm to this language

such that if M accepts w then L(M') is L(G1), and otherwise it is PHI.

Where G1 is some CFG so that L(G1) is in C, of course using the same assumptions of PHI

as we did with Rice's theorem.

The reduction itself seems to work for me,

Now something must be wrong, but where?

Thanks.