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Metamath Proof Explorer

Theorem 19.25

Description: Theorem 19.25 of Margaris p. 90. (Contributed by NM, 12-Mar-1993)

Ref Expression
Assertion 19.25 
|- ( A. y E. x ( ph -> ps ) -> ( E. y A. x ph -> E. y E. x ps ) )

Proof

Step Hyp Ref Expression
1 19.35 
 |-  ( E. x ( ph -> ps ) <-> ( A. x ph -> E. x ps ) )
2 1 biimpi 
 |-  ( E. x ( ph -> ps ) -> ( A. x ph -> E. x ps ) )
3 2 aleximi 
 |-  ( A. y E. x ( ph -> ps ) -> ( E. y A. x ph -> E. y E. x ps ) )