Theorem 2alanimi 38571

Description: Removes two universal quantifiers from a statement. (Contributed by Andrew Salmon, 24-May-2011.)

Hypothesis

Ref	Expression
2alanimi.1	|- ( ( ph /\ ps ) -> ch )

Assertion

Ref	Expression
2alanimi	|- ( ( A. x A. y ph /\ A. x A. y ps ) -> A. x A. y ch )

Proof of Theorem 2alanimi

Step	Hyp	Ref	Expression
1		2alanimi.1	. . 3 |- ( ( ph /\ ps ) -> ch )
2	1	alanimi 1744	. 2 |- ( ( A. y ph /\ A. y ps ) -> A. y ch )
3	2	alanimi 1744	1 |- ( ( A. x A. y ph /\ A. x A. y ps ) -> A. x A. y ch )

Syntax hints:   -> wi 4   /\ wa 384   A.wal 1481

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737

This theorem depends on definitions:  df-bi 197  df-an 386

This theorem is referenced by: (None)