Theorem 2alimi 1689

Description: Inference doubly quantifying both antecedent and consequent. (Contributed by NM, 3-Feb-2005.)

Hypothesis

Ref	Expression
alimi.1	|- ( ph -> ps )

Assertion

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

Proof of Theorem 2alimi

Step	Hyp	Ref	Expression
1		alimi.1	. . 3 |- ( ph -> ps )
2	1	alimi 1688	. 2 |- ( A. y ph -> A. y ps )
3	2	alimi 1688	1 |- ( A. x A. y ph -> A. x A. y ps )

Syntax hints:   -> wi 4   A.wal 1446

This theorem was proved from axioms:  ax-mp 5  ax-gen 1673  ax-4 1686

This theorem is referenced by:  2mo  2381  2eu6  2388  euind  3193  reuind  3211  sbnfc2  3764  opelopabt  4686  ssrel  4901  ssrelrel  4913  opabbrex  6318  fnoprabg  6385  tz7.48lem  7145  ssrelf  28230  bj-3exbi  31209  bj-mo3OLD  31449  mpt2bi123f  32408  mptbi12f  32412  ismrc  35545  refimssco  36215  19.33-2  36732  pm11.63  36746  pm11.71  36748  axc5c4c711to11  36757