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How would I be able to show that the following are equivalenet:

a) x |= =| y

(b) For all Γ, Γ |= x <-> Γ |= y

(c) For all Γ and γ, we have Γ union {x} |= γ <-> Γ union {y} |= γ

I can prove a -> b and a -> c but I am having trouble proving b-> a and c-> a.

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