Theorem pm11.61 38593

Description: Theorem *11.61 in [WhiteheadRussell] p. 166. (Contributed by Andrew Salmon, 24-May-2011.)

Assertion

Ref	Expression
pm11.61	|- ( E. y A. x ( ph -> ps ) -> A. x ( ph -> E. y ps ) )

Distinct variable group:   ph, y

Allowed substitution hints:   ph( x)   ps( x, y)

Proof of Theorem pm11.61

Step	Hyp	Ref	Expression
1		19.12 2164	. 2 |- ( E. y A. x ( ph -> ps ) -> A. x E. y ( ph -> ps ) )
2		19.37v 1910	. . . 4 |- ( E. y ( ph -> ps ) <-> ( ph -> E. y ps ) )
3	2	biimpi 206	. . 3 |- ( E. y ( ph -> ps ) -> ( ph -> E. y ps ) )
4	3	alimi 1739	. 2 |- ( A. x E. y ( ph -> ps ) -> A. x ( ph -> E. y ps ) )
5	1, 4	syl 17	1 |- ( E. y A. x ( ph -> ps ) -> A. x ( ph -> E. y ps ) )

Syntax hints:   -> 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  ax-5 1839  ax-6 1888  ax-7 1935  ax-10 2019  ax-11 2034  ax-12 2047

This theorem depends on definitions:  df-bi 197  df-or 385  df-ex 1705  df-nf 1710

This theorem is referenced by: (None)