Theorem 2alimi 1386

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 1385	. 2 |- ( A. y ph -> A. y ps )
3	2	alimi 1385	1 |- ( A. x A. y ph -> A. x A. y ps )

Syntax hints:   -> wi 4   A.wal 1283

This theorem was proved from axioms:  ax-mp 7  ax-5 1377  ax-gen 1379

This theorem is referenced by:  mo23  1984  mo3h  1996  spc2gv  2699  spc3gv  2701  euind  2790  reuind  2806  sbnfc2  2973  opelopabt  4052  ssrel  4482  ssrelrel  4494  fnoprabg  5679