Theorem 19.40-2 1655

Description: Theorem *11.42 in [WhiteheadRussell] p. 163. Theorem 19.40 of [Margaris] p. 90 with 2 quantifiers. (Contributed by Andrew Salmon, 24-May-2011.)

Assertion

Ref	Expression
19.40-2	|- ( E. x E. y ( ph /\ ps ) -> ( E. x E. y ph /\ E. x E. y ps ) )

Proof of Theorem 19.40-2

Step	Hyp	Ref	Expression
1		19.40 1654	. . 3 |- ( E. y ( ph /\ ps ) -> ( E. y ph /\ E. y ps ) )
2	1	eximi 1623	. 2 |- ( E. x E. y ( ph /\ ps ) -> E. x ( E. y ph /\ E. y ps ) )
3		19.40 1654	. 2 |- ( E. x ( E. y ph /\ E. y ps ) -> ( E. x E. y ph /\ E. x E. y ps ) )
4	2, 3	syl 14	1 |- ( E. x E. y ( ph /\ ps ) -> ( E. x E. y ph /\ E. x E. y ps ) )

Syntax hints:   -> wi 4   /\ wa 104   E.wex 1515

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1470  ax-gen 1472  ax-ie1 1516  ax-ie2 1517  ax-4 1533  ax-ial 1557

This theorem depends on definitions:  df-bi 117

This theorem is referenced by: (None)