# A question on a presumably admissible/derivable rule for (usual) formal systems [closed]

Suppose formal system $X$ has the rule $\vdash\beta\Rightarrow\hspace{2pt}\vdash\gamma$. Is the rule $\vdash\alpha\wedge\beta\Rightarrow\hspace{2pt}\vdash\alpha\wedge\gamma$ (usually) just admissible and not derivable? How may we derive the rule $\vdash\alpha\wedge\beta\Rightarrow\hspace{2pt}\vdash\alpha\wedge\gamma$ if it is derivable?

Edit:

I now see that what I needed was $\vdash(\alpha\vee\lnot\gamma)\Rightarrow\hspace{2pt}\vdash(\alpha\vee\lnot\beta)$ on the condition that $\vdash\beta\Rightarrow\hspace{2pt}\vdash\gamma$. That would up to a point have been a meaningful question as opposed to the one I posed.I will delete this question later today.

## closed as off-topic by Frode Bjørdal, Todd Trimble♦Oct 25 '15 at 22:40

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question does not appear to be about research level mathematics within the scope defined in the help center." – Frode Bjørdal, Todd Trimble
If this question can be reworded to fit the rules in the help center, please edit the question.

• (Closed on request.) – Todd Trimble Oct 25 '15 at 22:40

• Kjos-Hansen I now see that what I needed was $\vdash(\alpha\vee\lnot\gamma)\Rightarrow\hspace{2pt}\vdash(\alpha\vee\lnot\beta)$ on the condition that $\vdash\beta\Rightarrow\hspace{2pt}\vdash\gamma$. That would up to a point have been a meaningful question as opposed to the one I posed. – Frode Bjørdal Oct 25 '15 at 13:51