Theorem rspa 2518

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 2517	. 2 |- ( A. x e. A ph -> ( x e. A -> ph ) )
2	1	imp 123	1 |- ( ( A. x e. A ph /\ x e. A ) -> ph )

Syntax hints:   -> wi 4   /\ wa 103   e. wcel 2141   A.wral 2448

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-4 1503

This theorem depends on definitions:  df-bi 116  df-ral 2453

This theorem is referenced by: (None)