Theorem 2alimi 1505

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 1504	. 2 |- ( A. y ph -> A. y ps )
3	2	alimi 1504	1 |- ( A. x A. y ph -> A. x A. y ps )

Syntax hints:   -> wi 4   A.wal 1396

This theorem was proved from axioms:  ax-mp 5  ax-5 1496  ax-gen 1498

This theorem is referenced by:  mo23  2121  mo3h  2133  spc2gv  2898  spc3gv  2900  euind  2994  reuind  3012  sbnfc2  3189  opelopabt  4362  ssrel  4820  ssrelrel  4832  fundif  5381  fnoprabg  6132