Theorem pm10.53 38565

Description: Theorem *10.53 in [WhiteheadRussell] p. 155. (Contributed by Andrew Salmon, 24-May-2011.)

Assertion

Ref	Expression
pm10.53	|- ( -. E. x ph -> A. x ( ph -> ps ) )

Proof of Theorem pm10.53

Step	Hyp	Ref	Expression
1		pm2.21 120	. 2 |- ( -. E. x ph -> ( E. x ph -> A. x ps ) )
2		19.38 1766	. 2 |- ( ( E. x ph -> A. x ps ) -> A. x ( ph -> ps ) )
3	1, 2	syl 17	1 |- ( -. E. x ph -> A. x ( ph -> ps ) )

Syntax hints:   -. wn 3   -> wi 4   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

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

This theorem is referenced by: (None)