Users' Mathboxes Mathbox for Jeff Madsen < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  rabeq12OLD Unicode version

Theorem rabeq12OLD 26453
Description: Equality of restricted class abstractions. (Moved to rabeqbidv 2796 in main set.mm and may be deleted by mathbox owner, JM. --NM 15-Sep-2011.) (Contributed by Jeff Madsen, 1-Dec-2009.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
rabeq12.1OLD  |-  ( ph  ->  A  =  B )
rabeq12.2OLD  |-  ( ph  ->  ( ps  <->  ch )
)
Assertion
Ref Expression
rabeq12OLD  |-  ( ph  ->  { x  e.  A  |  ps }  =  {
x  e.  B  |  ch } )
Distinct variable groups:    x, A    x, B    ph, x
Allowed substitution hints:    ps( x)    ch( x)

Proof of Theorem rabeq12OLD
StepHypRef Expression
1 rabeq12.1OLD . 2  |-  ( ph  ->  A  =  B )
2 rabeq12.2OLD . 2  |-  ( ph  ->  ( ps  <->  ch )
)
31, 2rabeqbidv 2796 1  |-  ( ph  ->  { x  e.  A  |  ps }  =  {
x  e.  B  |  ch } )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 176    = wceq 1632   {crab 2560
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-ral 2561  df-rab 2565
  Copyright terms: Public domain W3C validator