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Theorem pm13.195 26780
Description: Theorem *13.195 in [WhiteheadRussell] p. 179. This theorem is very similar to sbc5 2945. (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 2945 . 2  |-  ( [. A  /  y ]. ph  <->  E. y
( y  =  A  /\  ph ) )
21bicomi 195 1  |-  ( E. y ( y  =  A  /\  ph )  <->  [. A  /  y ]. ph )
Colors of variables: wff set class
Syntax hints:    <-> wb 178    /\ wa 360   E.wex 1537    = wceq 1619   [.wsbc 2921
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-7 1535  ax-gen 1536  ax-8 1623  ax-11 1624  ax-17 1628  ax-12o 1664  ax-10 1678  ax-9 1684  ax-4 1692  ax-16 1926  ax-ext 2234
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1315  df-ex 1538  df-nf 1540  df-sb 1883  df-clab 2240  df-cleq 2246  df-clel 2249  df-nfc 2374  df-v 2729  df-sbc 2922
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