Users' Mathboxes Mathbox for Stefan O'Rear < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  sbcrot3OLD Unicode version

Theorem sbcrot3OLD 26544
Description: Rotate a sequence of three explicit substitutions. Substituted values must be manifest sets. (Contributed by Stefan O'Rear, 11-Oct-2014.) (New usage is discouraged.) (Proof modification is discouraged.)
Hypotheses
Ref Expression
sbcrot3OLD.1  |-  A  e. 
_V
sbcrot3OLD.2  |-  B  e. 
_V
sbcrot3OLD.3  |-  C  e. 
_V
Assertion
Ref Expression
sbcrot3OLD  |-  ( [. A  /  a ]. [. B  /  b ]. [. C  /  c ]. ph  <->  [. B  / 
b ]. [. C  / 
c ]. [. A  / 
a ]. ph )
Distinct variable groups:    A, b    A, c    B, a    C, a   
a, c    a, b
Allowed substitution hints:    ph( a, b, c)    A( a)    B( b, c)    C( b, c)

Proof of Theorem sbcrot3OLD
StepHypRef Expression
1 sbcrot3 26540 1  |-  ( [. A  /  a ]. [. B  /  b ]. [. C  /  c ]. ph  <->  [. B  / 
b ]. [. C  / 
c ]. [. A  / 
a ]. ph )
Colors of variables: wff set class
Syntax hints:    <-> wb 177    e. wcel 1717   _Vcvv 2901   [.wsbc 3106
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1661  ax-8 1682  ax-6 1736  ax-7 1741  ax-11 1753  ax-12 1939  ax-ext 2370
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2376  df-cleq 2382  df-clel 2385  df-nfc 2514  df-v 2903  df-sbc 3107
  Copyright terms: Public domain W3C validator