Theorem 2exim 38578

Description: Theorem *11.34 in [WhiteheadRussell] p. 162. Theorem 19.22 of [Margaris] p. 90 with 2 quantifiers. (Contributed by Andrew Salmon, 24-May-2011.)

Assertion

Ref	Expression
2exim	|- ( A. x A. y ( ph -> ps ) -> ( E. x E. y ph -> E. x E. y ps ) )

Proof of Theorem 2exim

Step	Hyp	Ref	Expression
1		exim 1761	. 2 |- ( A. y ( ph -> ps ) -> ( E. y ph -> E. y ps ) )
2	1	aleximi 1759	1 |- ( A. x A. y ( ph -> ps ) -> ( E. x E. y ph -> E. x 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

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

This theorem is referenced by: (None)