Users' Mathboxes Mathbox for Andrew Salmon < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  2alanimi Structured version   Unicode version

Theorem 2alanimi 29767
Description: Removes two universal quantifiers from a statement. (Contributed by Andrew Salmon, 24-May-2011.)
Hypothesis
Ref Expression
2alanimi.1  |-  ( (
ph  /\  ps )  ->  ch )
Assertion
Ref Expression
2alanimi  |-  ( ( A. x A. y ph  /\  A. x A. y ps )  ->  A. x A. y ch )

Proof of Theorem 2alanimi
StepHypRef Expression
1 2alanimi.1 . . 3  |-  ( (
ph  /\  ps )  ->  ch )
21alanimi 1608 . 2  |-  ( ( A. y ph  /\  A. y ps )  ->  A. y ch )
32alanimi 1608 1  |-  ( ( A. x A. y ph  /\  A. x A. y ps )  ->  A. x A. y ch )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    /\ wa 369   A.wal 1368
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603
This theorem depends on definitions:  df-bi 185  df-an 371
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator