MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  sbcbiiOLD Unicode version

Theorem sbcbiiOLD 3060
Description: Formula-building inference rule for class substitution. (Contributed by NM, 11-Nov-2005.) (New usage is discouraged.)
Hypothesis
Ref Expression
sbcbii.1  |-  ( ph  <->  ps )
Assertion
Ref Expression
sbcbiiOLD  |-  ( A  e.  V  ->  ( [. A  /  x ]. ph  <->  [. A  /  x ]. ps ) )

Proof of Theorem sbcbiiOLD
StepHypRef Expression
1 sbcbii.1 . . 3  |-  ( ph  <->  ps )
21sbcbii 3059 . 2  |-  ( [. A  /  x ]. ph  <->  [. A  /  x ]. ps )
32a1i 10 1  |-  ( A  e.  V  ->  ( [. A  /  x ]. ph  <->  [. A  /  x ]. ps ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 176    e. wcel 1696   [.wsbc 3004
This theorem is referenced by:  isibg2  26213  2sbcrex  26967  sbc3org  28594  trsbc  28603  sbcssOLD  28605  eqsbc3rVD  28932  bnj89  29063  bnj524  29082  bnj984  29300  bnj1452  29398
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-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-sbc 3005
  Copyright terms: Public domain W3C validator