Users' Mathboxes Mathbox for Alan Sare < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  sbcbiiOLD Structured version   Unicode version

Theorem sbcbiiOLD 33711
Description: Formula-building inference rule for class substitution. (Contributed by NM, 11-Nov-2005.) Obsolete as of 17-Aug-2018. Use sbcbii 3380 instead. (New usage is discouraged.) (Proof modification is discouraged.)
Hypothesis
Ref Expression
sbcbiiOLD.1  |-  ( ph  <->  ps )
Assertion
Ref Expression
sbcbiiOLD  |-  ( A  e.  V  ->  ( [. A  /  x ]. ph  <->  [. A  /  x ]. ps ) )

Proof of Theorem sbcbiiOLD
StepHypRef Expression
1 sbcbiiOLD.1 . . 3  |-  ( ph  <->  ps )
21sbcbii 3380 . 2  |-  ( [. A  /  x ]. ph  <->  [. A  /  x ]. ps )
32a1i 11 1  |-  ( A  e.  V  ->  ( [. A  /  x ]. ph  <->  [. A  /  x ]. ps ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    <-> wb 184    e. wcel 1823   [.wsbc 3324
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1623  ax-4 1636  ax-5 1709  ax-6 1752  ax-7 1795  ax-10 1842  ax-11 1847  ax-12 1859  ax-13 2004  ax-ext 2432
This theorem depends on definitions:  df-bi 185  df-an 369  df-tru 1401  df-ex 1618  df-nf 1622  df-sb 1745  df-clab 2440  df-cleq 2446  df-clel 2449  df-sbc 3325
This theorem is referenced by:  sbc3orgOLD  33712  sbcssOLD  33726  eqsbc3rVD  34059
  Copyright terms: Public domain W3C validator