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

Theorem sbcbiiOLD 3392
Description: Formula-building inference rule for class substitution. (Contributed by NM, 11-Nov-2005.) Obsolete as of 17-Aug-2018. Use sbcbii 3391 instead. (New usage is discouraged.) (Proof modification 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 3391 . 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 1767   [.wsbc 3331
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-10 1786  ax-11 1791  ax-12 1803  ax-13 1968  ax-ext 2445
This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1382  df-ex 1597  df-nf 1600  df-sb 1712  df-clab 2453  df-cleq 2459  df-clel 2462  df-sbc 3332
This theorem is referenced by:  sbc3orgOLD  32599  sbcssOLD  32610  eqsbc3rVD  32937
  Copyright terms: Public domain W3C validator