Theorem 2alimi 1345

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 1344	. 2 |- ( A. y ph -> A. y ps )
3	2	alimi 1344	1 |- ( A. x A. y ph -> A. x A. y ps )

Syntax hints:   -> wi 4   A.wal 1241

This theorem was proved from axioms:  ax-mp 7  ax-5 1336  ax-gen 1338

This theorem is referenced by:  mo23  1941  mo3h  1953  spc2gv  2643  spc3gv  2645  euind  2728  reuind  2744  sbnfc2  2906  opelopabt  3999  ssrel  4428  ssrelrel  4440  fnoprabg  5602