Theorem 2exnaln 1756

Description: Theorem *11.22 in [WhiteheadRussell] p. 160. (Contributed by Andrew Salmon, 24-May-2011.)

Assertion

Ref	Expression
2exnaln	|- ( E. x E. y ph <-> -. A. x A. y -. ph )

Proof of Theorem 2exnaln

Step	Hyp	Ref	Expression
1		df-ex 1705	. 2 |- ( E. x E. y ph <-> -. A. x -. E. y ph )
2		alnex 1706	. . 3 |- ( A. y -. ph <-> -. E. y ph )
3	2	albii 1747	. 2 |- ( A. x A. y -. ph <-> A. x -. E. y ph )
4	1, 3	xchbinxr 325	1 |- ( E. x E. y ph <-> -. A. x A. y -. ph )

Syntax hints:   -. wn 3   <-> 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

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

This theorem is referenced by:  2nexaln  1757  excom  2042  cbvex2  2280  opab0  5007  bj-modal4e  32705  bj-cbvex2v  32738