Theorem ra42 1245

Description: Restricted specialization.

Assertion

Ref	Expression
ra42	|- (A.x e. A A.y e. B ph -> ((x e. A /\ y e. B) -> ph))

Proof of Theorem ra42

Step	Hyp	Ref	Expression
1		ra4 1243	. . 3 |- (A.x e. A A.y e. B ph -> (x e. A -> A.y e. B ph))
2		ra4 1243	. . 3 |- (A.y e. B ph -> (y e. B -> ph))
3	1, 2	syl6 23	. 2 |- (A.x e. A A.y e. B ph -> (x e. A -> (y e. B -> ph)))
4	3	imp3a 279	1 |- (A.x e. A A.y e. B ph -> ((x e. A /\ y e. B) -> ph))

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

This theorem is referenced by:  solin 2145  ralxp 2456  f1fveq 2918  isotrALT 2936

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

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