Theorem 19.40-2 1814

Description: Theorem *11.42 in [WhiteheadRussell] p. 163. Theorem 19.40 of [Margaris] p. 90 with two 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 1797	. . 3 |- ( E. y ( ph /\ ps ) -> ( E. y ph /\ E. y ps ) )
2	1	eximi 1762	. 2 |- ( E. x E. y ( ph /\ ps ) -> E. x ( E. y ph /\ E. y ps ) )
3		19.40 1797	. 2 |- ( E. x ( E. y ph /\ E. y ps ) -> ( E. x E. y ph /\ E. x E. y ps ) )
4	2, 3	syl 17	1 |- ( E. x E. y ( ph /\ ps ) -> ( E. x E. y ph /\ E. x E. y ps ) )

Syntax hints:   -> wi 4   /\ wa 384   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-an 386  df-ex 1705

This theorem is referenced by: (None)