ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  2alimi Unicode version

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
StepHypRef Expression
1 alimi.1 . . 3  |-  ( ph  ->  ps )
21alimi 1385 . 2  |-  ( A. y ph  ->  A. y ps )
32alimi 1385 1  |-  ( A. x A. y ph  ->  A. x A. y ps )
Colors of variables: wff set class
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
  Copyright terms: Public domain W3C validator