Theorem spsbce-2

Description: Theorem *11.36 in WhiteheadRussell p. 162. (Contributed by Andrew Salmon, 24-May-2011)

	Ref	Expression
Assertion	spsbce-2	|- ( [ z / x ] [ w / y ] ph -> E. x E. y ph )

Proof

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