Theorem spsbce-2 38580

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

Step	Hyp	Ref	Expression
1		spsbe 1884	. 2 |- ( [ z / x ] [ w / y ] ph -> E. x [ w / y ] ph )
2		spsbe 1884	. . 3 |- ( [ w / y ] ph -> E. y ph )
3	2	eximi 1762	. 2 |- ( E. x [ w / y ] ph -> E. x E. y ph )
4	1, 3	syl 17	1 |- ( [ z / x ] [ w / y ] ph -> E. x E. y ph )

Syntax hints:   -> wi 4   E.wex 1704   [wsb 1880

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737

This theorem depends on definitions:  df-bi 197  df-an 386  df-ex 1705  df-sb 1881

This theorem is referenced by: (None)