Theorem 19.29r2 1553

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 1552	. 2 |- ( ( E. x E. y ph /\ A. x A. y ps ) -> E. x ( E. y ph /\ A. y ps ) )
2		19.29r 1552	. . 3 |- ( ( E. y ph /\ A. y ps ) -> E. y ( ph /\ ps ) )
3	2	eximi 1531	. 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 102   A.wal 1282   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)