Theorem 2nexaln 1757

Description: Theorem *11.25 in [WhiteheadRussell] p. 160. (Contributed by Andrew Salmon, 24-May-2011.)

Assertion

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

Proof of Theorem 2nexaln

Step	Hyp	Ref	Expression
1		2exnaln 1756	. . 3 |- ( E. x E. y ph <-> -. A. x A. y -. ph )
2	1	bicomi 214	. 2 |- ( -. A. x A. y -. ph <-> E. x E. y ph )
3	2	con1bii 346	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:  2mo  2551  bj-alcomexcom  32670  pm11.63  38595  fun2dmnopgexmpl  41303  spr0nelg  41726