## Are the two LTL properties $GF(\psi_1 \land F\psi_2 )$ and $GF(\psi_2 \land F\psi_1 )$ equivalent?

Is $$GF(\psi_1 \land F\psi_2 )$$ equivalent to the property $$GF(\psi_2 \land F\psi_1 )$$?

Attempt:

In the first property each state must eventually see $$\psi_1$$ and $$\psi_2$$, in the second property as well each state must eventually see $$\psi_1$$ and $$\psi_2$$, as such the two properties must be equivalent. Is this correct?