Theorem eximdh

Deduction from Theorem 19.22 of [Margaris] p. 90. (Contributed by NM, 20-May-1996.)

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