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Theorem pm13.195 36401
Description: Theorem *13.195 in [WhiteheadRussell] p. 179. This theorem is very similar to sbc5 3330. (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 3330 . 2  |-  ( [. A  /  y ]. ph  <->  E. y
( y  =  A  /\  ph ) )
21bicomi 205 1  |-  ( E. y ( y  =  A  /\  ph )  <->  [. A  /  y ]. ph )
Colors of variables: wff setvar class
Syntax hints:    <-> wb 187    /\ wa 370    = wceq 1437   E.wex 1659   [.wsbc 3305
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-5 1751  ax-6 1797  ax-7 1841  ax-10 1889  ax-12 1907  ax-13 2055  ax-ext 2407
This theorem depends on definitions:  df-bi 188  df-an 372  df-tru 1440  df-ex 1660  df-nf 1664  df-sb 1790  df-clab 2415  df-cleq 2421  df-clel 2424  df-v 3089  df-sbc 3306
This theorem is referenced by: (None)
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