Theorem 2exanali 38587

Description: Theorem *11.521 in [WhiteheadRussell] p. 164. (Contributed by Andrew Salmon, 24-May-2011.)

Assertion

Ref	Expression
2exanali	|- ( -. E. x E. y ( ph /\ -. ps ) <-> A. x A. y ( ph -> ps ) )

Proof of Theorem 2exanali

Step	Hyp	Ref	Expression
1		2nalexn 1755	. . 3 |- ( -. A. x A. y ( ph -> ps ) <-> E. x E. y -. ( ph -> ps ) )
2	1	con1bii 346	. 2 |- ( -. E. x E. y -. ( ph -> ps ) <-> A. x A. y ( ph -> ps ) )
3		annim 441	. . 3 |- ( ( ph /\ -. ps ) <-> -. ( ph -> ps ) )
4	3	2exbii 1775	. 2 |- ( E. x E. y ( ph /\ -. ps ) <-> E. x E. y -. ( ph -> ps ) )
5	2, 4	xchnxbir 323	1 |- ( -. E. x E. y ( ph /\ -. ps ) <-> A. x A. y ( ph -> ps ) )

Syntax hints:   -. wn 3   -> wi 4   <-> wb 196   /\ wa 384   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-an 386  df-ex 1705

This theorem is referenced by: (None)