Theorem pm10.52 38564

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

Assertion

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

Distinct variable group:   ps, x

Allowed substitution hint:   ph( x)

Proof of Theorem pm10.52

Step	Hyp	Ref	Expression
1		19.23v 1902	. 2 |- ( A. x ( ph -> ps ) <-> ( E. x ph -> ps ) )
2		pm5.5 351	. 2 |- ( E. x ph -> ( ( E. x ph -> ps ) <-> ps ) )
3	1, 2	syl5bb 272	1 |- ( E. x ph -> ( A. x ( ph -> ps ) <-> ps ) )

Syntax hints:   -> wi 4   <-> wb 196   A.wal 1481   E.wex 1704

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888

This theorem depends on definitions:  df-bi 197  df-ex 1705

This theorem is referenced by: (None)