Theorem 2al2imi 38572

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

Hypothesis

Ref	Expression
2al2imi.1	|- ( ph -> ( ps -> ch ) )

Assertion

Ref	Expression
2al2imi	|- ( A. x A. y ph -> ( A. x A. y ps -> A. x A. y ch ) )

Proof of Theorem 2al2imi

Step	Hyp	Ref	Expression
1		2al2imi.1	. . 3 |- ( ph -> ( ps -> ch ) )
2	1	al2imi 1743	. 2 |- ( A. y ph -> ( A. y ps -> A. y ch ) )
3	2	al2imi 1743	1 |- ( A. x A. y ph -> ( A. x A. y ps -> A. x A. y ch ) )

Syntax hints:   -> wi 4   A.wal 1481

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

This theorem is referenced by:  2alim  38576