Theorem alrimdh

Deduction form of Theorem 19.21 of [Margaris] p. 90, see 19.21 and 19.21h. (Contributed by NM, 10-Feb-1997.) (Proof shortened by Andrew Salmon, 13-May-2011.)

Hypotheses
alrimdh.1
\( \vdash \varphi \rightarrow \forall x \, \varphi \)
alrimdh.2
\( \vdash \psi \rightarrow \forall x \, \psi \)
alrimdh.3
\( \vdash \varphi \rightarrow \psi \rightarrow \chi \)
Conclusion
\( \vdash \varphi \rightarrow \psi \rightarrow \forall x \, \chi \)
Proof
l0
alrimdh.2
\( \vdash \psi \rightarrow \forall x \, \psi \)
l1
alrimdh.1
alrimdh.3
alimdh l1 _
\( \vdash \varphi \rightarrow \forall x \, \psi \rightarrow \forall x \, \chi \)
syl5 l0 _