Theorem 2alimi 1679

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 1678	. 2 |- ( A. y ph -> A. y ps )
3	2	alimi 1678	1 |- ( A. x A. y ph -> A. x A. y ps )

Syntax hints:   -> wi 4   A.wal 1435

This theorem was proved from axioms:  ax-mp 5  ax-gen 1663  ax-4 1676

This theorem is referenced by:  2mo  2350  2eu6  2357  euind  3257  reuind  3275  sbnfc2  3826  opelopabt  4732  ssrel  4942  ssrelrel  4954  opabbrex  6347  fnoprabg  6411  tz7.48lem  7169  ssrelf  28223  bj-3exbi  31206  bj-mo3OLD  31417  mpt2bi123f  32370  mptbi12f  32374  ismrc  35512  refimssco  36183  19.33-2  36701  pm11.63  36715  pm11.71  36717  axc5c4c711to11  36726