Theorem alrimdd

Deduction form of Theorem 19.21 of [Margaris] p. 90, see 19.21. (Contributed by Mario Carneiro, 24-Sep-2016.)

Hypotheses
alrimdd.1
\( \vdash \Finv x \, \varphi \)
alrimdd.2
\( \vdash \varphi \rightarrow \Finv x \, \psi \)
alrimdd.3
\( \vdash \varphi \rightarrow \psi \rightarrow \chi \)
Conclusion
\( \vdash \varphi \rightarrow \psi \rightarrow \forall x \, \chi \)
Proof
alrimdd.2
l1
nf5rd _
\( \vdash \varphi \rightarrow \psi \rightarrow \forall x \, \psi \)
l2
alrimdd.1
alrimdd.3
alimd l2 _
\( \vdash \varphi \rightarrow \forall x \, \psi \rightarrow \forall x \, \chi \)
syld l1 _