Theorem rspec2 1267

Description: Specialization rule for restricted quantification.

Hypothesis

Ref	Expression
rspec2.1	|- A.x e. A A.y e. B ph

Assertion

Ref	Expression
rspec2	|- ((x e. A /\ y e. B) -> ph)

Proof of Theorem rspec2

Step	Hyp	Ref	Expression
1		rspec2.1	. . 3 |- A.x e. A A.y e. B ph
2	1	rspec 1246	. 2 |- (x e. A -> A.y e. B ph)
3	2	r19.21bi 1266	1 |- ((x e. A /\ y e. B) -> ph)

Syntax hints:   -> wi 2   /\ wa 196   e. wcel 1092  A.wral 1201

This theorem is referenced by:  rspec3 1268

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6  ax-4 673

This theorem depends on definitions:  df-bi 128  df-an 198  df-ral 1205

metamath.org