Theorem 2exnexn 1772

Description: Theorem *11.51 in [WhiteheadRussell] p. 164. (Contributed by Andrew Salmon, 24-May-2011.) (Proof shortened by Wolf Lammen, 25-Sep-2014.)

Assertion

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

Proof of Theorem 2exnexn

Step	Hyp	Ref	Expression
1		alexn 1771	. 2 |- ( A. x E. y -. ph <-> -. E. x A. y ph )
2	1	con2bii 347	1 |- ( E. x A. y ph <-> -. A. x E. 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: (None)