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Metamath Proof Explorer

Theorem 19.29x

Description: Variation of 19.29 with mixed quantification. (Contributed by NM, 11-Feb-2005)

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

Proof

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