Users' Mathboxes Mathbox for Andrew Salmon < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  stdpc4-2 Unicode version

Theorem stdpc4-2 27569
Description: Theorem *11.1 in [WhiteheadRussell] p. 159. (Contributed by Andrew Salmon, 24-May-2011.)
Assertion
Ref Expression
stdpc4-2  |-  ( A. x A. y ph  ->  [ z  /  x ] [ w  /  y ] ph )

Proof of Theorem stdpc4-2
StepHypRef Expression
1 stdpc4 1964 . . 3  |-  ( A. y ph  ->  [ w  /  y ] ph )
21alimi 1546 . 2  |-  ( A. x A. y ph  ->  A. x [ w  / 
y ] ph )
3 stdpc4 1964 . 2  |-  ( A. x [ w  /  y ] ph  ->  [ z  /  x ] [ w  /  y ] ph )
42, 3syl 15 1  |-  ( A. x A. y ph  ->  [ z  /  x ] [ w  /  y ] ph )
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1527   [wsb 1629
This theorem is referenced by:  pm11.11  27570
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866
This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1529  df-sb 1630
  Copyright terms: Public domain W3C validator