Theorem 2alimi 1740

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 1739	. 2 |- ( A. y ph -> A. y ps )
3	2	alimi 1739	1 |- ( A. x A. y ph -> A. x A. y ps )

Syntax hints:   -> wi 4   A.wal 1481

This theorem was proved from axioms:  ax-mp 5  ax-gen 1722  ax-4 1737

This theorem is referenced by:  2mo  2551  2eu6  2558  euind  3393  reuind  3411  sbnfc2  4007  opelopabt  4987  ssrel  5207  ssrelOLD  5208  ssrelrel  5220  fundif  5935  opabbrex  6695  fnoprabg  6761  tz7.48lem  7536  ssrelf  29425  bj-3exbi  32600  bj-mo3OLD  32832  mpt2bi123f  33971  mptbi12f  33975  ismrc  37264  refimssco  37913  19.33-2  38581  pm11.63  38595  pm11.71  38597  axc5c4c711to11  38606