Theorem alimdh

Deduction form of Theorem 19.20 of [Margaris] p. 90, see alim. (Contributed by NM, 4-Jan-2002.)

Hypotheses
alimdh.1
\( \vdash \varphi \rightarrow \forall x \, \varphi \)
alimdh.2
\( \vdash \varphi \rightarrow \psi \rightarrow \chi \)
Conclusion
\( \vdash \varphi \rightarrow \forall x \, \psi \rightarrow \forall x \, \chi \)
Proof
l0
alimdh.1
\( \vdash \varphi \rightarrow \forall x \, \varphi \)
alimdh.2
al2imi _
\( \vdash \forall x \, \varphi \rightarrow \forall x \, \psi \rightarrow \forall x \, \chi \)
syl l0 _