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Theorem a4sbce-2 26745
Description: Theorem *11.36 in [WhiteheadRussell] p. 162. (Contributed by Andrew Salmon, 24-May-2011.)
Assertion
Ref Expression
a4sbce-2  |-  ( [ z  /  x ] [ w  /  y ] ph  ->  E. x E. y ph )

Proof of Theorem a4sbce-2
StepHypRef Expression
1 a4sbe 1967 . 2  |-  ( [ z  /  x ] [ w  /  y ] ph  ->  E. x [ w  /  y ] ph )
2 a4sbe 1967 . . 3  |-  ( [ w  /  y ]
ph  ->  E. y ph )
32eximi 1574 . 2  |-  ( E. x [ w  / 
y ] ph  ->  E. x E. y ph )
41, 3syl 17 1  |-  ( [ z  /  x ] [ w  /  y ] ph  ->  E. x E. y ph )
Colors of variables: wff set class
Syntax hints:    -> wi 6   E.wex 1537   [wsb 1882
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
This theorem depends on definitions:  df-bi 179  df-an 362  df-tru 1315  df-ex 1538  df-nf 1540  df-sb 1883
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