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Theorem spsbce-2 27579
Description: Theorem *11.36 in [WhiteheadRussell] p. 162. (Contributed by Andrew Salmon, 24-May-2011.)
Assertion
Ref Expression
spsbce-2  |-  ( [ z  /  x ] [ w  /  y ] ph  ->  E. x E. y ph )

Proof of Theorem spsbce-2
StepHypRef Expression
1 spsbe 2015 . 2  |-  ( [ z  /  x ] [ w  /  y ] ph  ->  E. x [ w  /  y ] ph )
2 spsbe 2015 . . 3  |-  ( [ w  /  y ]
ph  ->  E. y ph )
32eximi 1563 . 2  |-  ( E. x [ w  / 
y ] ph  ->  E. x E. y ph )
41, 3syl 15 1  |-  ( [ z  /  x ] [ w  /  y ] ph  ->  E. x E. y ph )
Colors of variables: wff set class
Syntax hints:    -> wi 4   E.wex 1528   [wsb 1629
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866
This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630
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