Users' Mathboxes Mathbox for Stefan O'Rear < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  sbcrot5OLD Unicode version

Theorem sbcrot5OLD 26976
Description: Rotate a sequence of five explicit substitutions. Substituted values must be manifest sets. (Contributed by Stefan O'Rear, 11-Oct-2014.)
Hypotheses
Ref Expression
sbcrot3OLD.1  |-  A  e. 
_V
sbcrot3OLD.2  |-  B  e. 
_V
sbcrot3OLD.3  |-  C  e. 
_V
sbcrot5OLD.4  |-  D  e. 
_V
sbcrot5OLD.5  |-  E  e. 
_V
Assertion
Ref Expression
sbcrot5OLD  |-  ( [. A  /  a ]. [. B  /  b ]. [. C  /  c ]. [. D  /  d ]. [. E  /  e ]. ph  <->  [. B  / 
b ]. [. C  / 
c ]. [. D  / 
d ]. [. E  / 
e ]. [. A  / 
a ]. ph )
Distinct variable groups:    A, b    A, c    B, a    C, a   
a, c    a, b    A, d    A, e    D, a    E, a    e, a    a,
d
Allowed substitution hints:    ph( e, a, b, c, d)    A( a)    B( e, b, c, d)    C( e, b, c, d)    D( e, b, c, d)    E( e, b, c, d)

Proof of Theorem sbcrot5OLD
StepHypRef Expression
1 sbcrot5 26972 1  |-  ( [. A  /  a ]. [. B  /  b ]. [. C  /  c ]. [. D  /  d ]. [. E  /  e ]. ph  <->  [. B  / 
b ]. [. C  / 
c ]. [. D  / 
d ]. [. E  / 
e ]. [. A  / 
a ]. ph )
Colors of variables: wff set class
Syntax hints:    <-> wb 176    e. wcel 1696   _Vcvv 2801   [.wsbc 3004
This theorem is referenced by:  6rexfrabdioph  26983  7rexfrabdioph  26984
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-v 2803  df-sbc 3005
  Copyright terms: Public domain W3C validator