Theorem 2alimdv 1802

Description: Deduction from Theorem 19.22 of [Margaris] p. 90. (Contributed by NM, 27-Apr-2004.)

Hypothesis

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

Assertion

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

Distinct variable groups:   ph, x   ph, y

Allowed substitution hints:   ps( x, y)   ch( x, y)

Proof of Theorem 2alimdv

Step	Hyp	Ref	Expression
1		2alimdv.1	. . 3 |- ( ph -> ( ps -> ch ) )
2	1	alimdv 1800	. 2 |- ( ph -> ( A. y ps -> A. y ch ) )
3	2	alimdv 1800	1 |- ( ph -> ( A. x A. y ps -> A. x A. y ch ) )

Syntax hints:   -> wi 4   A.wal 1282

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-5 1376  ax-gen 1378  ax-17 1459

This theorem is referenced by:  moimv  2007  soss  4069