Theorem rspa 2542

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 2541	. 2 |- ( A. x e. A ph -> ( x e. A -> ph ) )
2	1	imp 124	1 |- ( ( A. x e. A ph /\ x e. A ) -> ph )

Syntax hints:   -> wi 4   /\ wa 104   e. wcel 2164   A.wral 2472

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-4 1521

This theorem depends on definitions:  df-bi 117  df-ral 2477

This theorem is referenced by:  gausslemma2dlem6  15131