Theorem al2imi

Inference quantifying antecedent, nested antecedent, and consequent. (Contributed by NM, 10-Jan-1993.)

Hypothesis
al2imi.1
\( \vdash \varphi \rightarrow \psi \rightarrow \chi \)
Conclusion
\( \vdash \forall x \, \varphi \rightarrow \forall x \, \psi \rightarrow \forall x \, \chi \)
Proof
l0
al2im
\( \vdash \forall x \, (\varphi \rightarrow \psi \rightarrow \chi) \rightarrow \forall x \, \varphi \rightarrow \forall x \, \psi \rightarrow \forall x \, \chi \)
al2imi.1
\( \vdash \varphi \rightarrow \psi \rightarrow \chi \)
mpg l0 _