Theorem 19.40-2 1563

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 1562	. . 3 |- ( E. y ( ph /\ ps ) -> ( E. y ph /\ E. y ps ) )
2	1	eximi 1531	. 2 |- ( E. x E. y ( ph /\ ps ) -> E. x ( E. y ph /\ E. y ps ) )
3		19.40 1562	. 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 102   E.wex 1421

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1376  ax-gen 1378  ax-ie1 1422  ax-ie2 1423  ax-4 1440  ax-ial 1467

This theorem depends on definitions:  df-bi 115

This theorem is referenced by: (None)