Theorem pm11.63 38595

Description: Theorem *11.63 in [WhiteheadRussell] p. 166. (Contributed by Andrew Salmon, 24-May-2011.)

Assertion

Ref	Expression
pm11.63	|- ( -. E. x E. y ph -> A. x A. y ( ph -> ps ) )

Proof of Theorem pm11.63

Step	Hyp	Ref	Expression
1		2nexaln 1757	. 2 |- ( -. E. x E. y ph <-> A. x A. y -. ph )
2		pm2.21 120	. . 3 |- ( -. ph -> ( ph -> ps ) )
3	2	2alimi 1740	. 2 |- ( A. x A. y -. ph -> A. x A. y ( ph -> ps ) )
4	1, 3	sylbi 207	1 |- ( -. E. x E. y ph -> A. x A. y ( 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)