Theorem pm10.52

Description: Theorem *10.52 in WhiteheadRussell p. 155. (Contributed by Andrew Salmon, 24-May-2011)

	Ref	Expression
Assertion	pm10.52	|- ( E. x ph -> ( A. x ( ph -> ps ) <-> ps ) )

Proof

Step	Hyp	Ref	Expression
1		19.23v	|- ( A. x ( ph -> ps ) <-> ( E. x ph -> ps ) )
2		pm5.5	|- ( E. x ph -> ( ( E. x ph -> ps ) <-> ps ) )
3	1 2	syl5bb	|- ( E. x ph -> ( A. x ( ph -> ps ) <-> ps ) )