Theorem rspa 2598

Description: Restricted specialization. (Contributed by Glauco Siliprandi, 11-Dec-2019.)

Assertion

Ref	Expression
rspa	|- ( ( A. x e. A ph /\ x e. A ) -> ph )

Proof of Theorem rspa

Step	Hyp	Ref	Expression
1		rsp 2597	. 2 |- ( A. x e. A ph -> ( x e. A -> ph ) )
2	1	imp 124	1 |- ( ( A. x e. A ph /\ x e. A ) -> ph )

This proof depends on syntax axioms:   -> wi 4   /\ wa 104   e. wcel 2209   A.wral 2528

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-4 1563

This proof depends on definitions:  df-bi 117  df-ral 2533

This theorem is used by:  abrexss  6358  gausslemma2dlem6  16186