Theorem 2alimi 1390

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 1389	. 2 |- ( A. y ph -> A. y ps )
3	2	alimi 1389	1 |- ( A. x A. y ph -> A. x A. y ps )

Syntax hints:   -> wi 4   A.wal 1287

This theorem was proved from axioms:  ax-mp 7  ax-5 1381  ax-gen 1383

This theorem is referenced by:  mo23  1989  mo3h  2001  spc2gv  2709  spc3gv  2711  euind  2802  reuind  2820  sbnfc2  2988  opelopabt  4089  ssrel  4526  ssrelrel  4538  fnoprabg  5746