Theorem 19.29r2 1615

Description: Variation of Theorem 19.29 of [Margaris] p. 90 with double quantification. (Contributed by NM, 3-Feb-2005.)

Assertion

Ref	Expression
19.29r2	|- ( ( E. x E. y ph /\ A. x A. y ps ) -> E. x E. y ( ph /\ ps ) )

Proof of Theorem 19.29r2

Step	Hyp	Ref	Expression
1		19.29r 1614	. 2 |- ( ( E. x E. y ph /\ A. x A. y ps ) -> E. x ( E. y ph /\ A. y ps ) )
2		19.29r 1614	. . 3 |- ( ( E. y ph /\ A. y ps ) -> E. y ( ph /\ ps ) )
3	2	eximi 1593	. 2 |- ( E. x ( E. y ph /\ A. y ps ) -> E. x E. y ( ph /\ ps ) )
4	1, 3	syl 14	1 |- ( ( E. x E. y ph /\ A. x A. y ps ) -> E. x E. y ( ph /\ ps ) )

Syntax hints:   -> wi 4   /\ wa 103   A.wal 1346   E.wex 1485

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1440  ax-gen 1442  ax-ie1 1486  ax-ie2 1487  ax-4 1503  ax-ial 1527

This theorem depends on definitions:  df-bi 116

This theorem is referenced by: (None)