Metamath Proof Explorer


Theorem ralim

Description: Distribution of restricted quantification over implication. (Contributed by NM, 9-Feb-1997) (Proof shortened by Wolf Lammen, 1-Dec-2019)

Ref Expression
Assertion ralim xAφψxAφxAψ

Proof

Step Hyp Ref Expression
1 id φψφψ
2 1 ral2imi xAφψxAφxAψ