Give proofs for the theorems of ℱ^ωstated below. Use appropriate analogues of the derived rules

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Step 1:u000AUnderstand the theorem to be proved:u000AWe need to prove that if $x_u005Ctau u003D y_u005Ctau$, then $S

Give proofs for the theorems of $\mathscr{F}^\omega$ stated below. Use appropriate analogues of the derived rules of inference of $$\$ 21$$. $\vdash x_\tau=y_\tau \supset . S_{x_\tau}^{x_\tau} A \supset S_{x_\tau}^{z_\tau} A$ provided $x_\tau$ and $y_\tau$ are free for $z_\tau$ in $A$.