Theorem 19.37vv 38584

Description: Theorem *11.46 in [WhiteheadRussell] p. 164. Theorem 19.37 of [Margaris] p. 90 with 2 quantifiers. (Contributed by Andrew Salmon, 24-May-2011.)

Assertion

Ref	Expression
19.37vv	|- ( E. x E. y ( ps -> ph ) <-> ( ps -> E. x E. y ph ) )

Distinct variable groups:   ps, x   ps, y

Allowed substitution hints:   ph( x, y)

Proof of Theorem 19.37vv

Step	Hyp	Ref	Expression
1		19.37v 1910	. . 3 |- ( E. y ( ps -> ph ) <-> ( ps -> E. y ph ) )
2	1	exbii 1774	. 2 |- ( E. x E. y ( ps -> ph ) <-> E. x ( ps -> E. y ph ) )
3		19.37v 1910	. 2 |- ( E. x ( ps -> E. y ph ) <-> ( ps -> E. x E. y ph ) )
4	2, 3	bitri 264	1 |- ( E. x E. y ( ps -> ph ) <-> ( ps -> E. x E. y ph ) )

Syntax hints:   -> wi 4   <-> wb 196   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  ax-5 1839  ax-6 1888

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

This theorem is referenced by: (None)