Users' Mathboxes Mathbox for Andrew Salmon < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  pm13.195 Unicode version

Theorem pm13.195 27716
Description: Theorem *13.195 in [WhiteheadRussell] p. 179. This theorem is very similar to sbc5 3028. (Contributed by Andrew Salmon, 3-Jun-2011.) (Revised by NM, 4-Jan-2017.)
Assertion
Ref Expression
pm13.195  |-  ( E. y ( y  =  A  /\  ph )  <->  [. A  /  y ]. ph )
Distinct variable group:    y, A
Allowed substitution hint:    ph( y)

Proof of Theorem pm13.195
StepHypRef Expression
1 sbc5 3028 . 2  |-  ( [. A  /  y ]. ph  <->  E. y
( y  =  A  /\  ph ) )
21bicomi 193 1  |-  ( E. y ( y  =  A  /\  ph )  <->  [. A  /  y ]. ph )
Colors of variables: wff set class
Syntax hints:    <-> wb 176    /\ wa 358   E.wex 1531    = wceq 1632   [.wsbc 3004
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-v 2803  df-sbc 3005
  Copyright terms: Public domain W3C validator