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Theorem pm13.195 30926
Description: Theorem *13.195 in [WhiteheadRussell] p. 179. This theorem is very similar to sbc5 3356. (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 3356 . 2  |-  ( [. A  /  y ]. ph  <->  E. y
( y  =  A  /\  ph ) )
21bicomi 202 1  |-  ( E. y ( y  =  A  /\  ph )  <->  [. A  /  y ]. ph )
Colors of variables: wff setvar class
Syntax hints:    <-> wb 184    /\ wa 369    = wceq 1379   E.wex 1596   [.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-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-v 3115  df-sbc 3332
This theorem is referenced by: (None)
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