Theorem 2alimdv 1847

Description: Deduction form of Theorem 19.20 of [Margaris] p. 90 with two quantifiers, see alim 1738. (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 1845	. 2 |- ( ph -> ( A. y ps -> A. y ch ) )
3	2	alimdv 1845	1 |- ( 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  ax-5 1839

This theorem is referenced by:  soss  5053  dfwe2  6981  tz7.48lem  7536  ss2mcls  31465  mclsax  31466