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Nov
19
revised Show that if $\vDash\Phi \to \Psi$ then $\vDash\forall x.\Phi \to \forall x.\Psi$
edited body
Nov
19
awarded  Editor
Nov
19
comment Show that if $\vDash\Phi \to \Psi$ then $\vDash\forall x.\Phi \to \forall x.\Psi$
I said that since all arbitrary $I,\theta\vDash\Phi \to \Psi$ we can say that $I,\theta[x/y]\vDash\Phi \to \Psi$ as well. Can I say this or am I misunderstanding what you mean?
Nov
19
revised Show that if $\vDash\Phi \to \Psi$ then $\vDash\forall x.\Phi \to \forall x.\Psi$
added 10 characters in body
Nov
19
awarded  Student
Nov
19
asked Show that if $\vDash\Phi \to \Psi$ then $\vDash\forall x.\Phi \to \forall x.\Psi$