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Metamath Proof Explorer

Theorem 19.39

Description: Theorem 19.39 of Margaris p. 90. (Contributed by NM, 12-Mar-1993)

Ref Expression
Assertion 19.39 
|- ( ( E. x ph -> E. x ps ) -> E. x ( ph -> ps ) )

Proof

Step Hyp Ref Expression
1 19.2 
 |-  ( A. x ph -> E. x ph )
2 1 imim1i 
 |-  ( ( E. x ph -> E. x ps ) -> ( A. x ph -> E. x ps ) )
3 19.35 
 |-  ( E. x ( ph -> ps ) <-> ( A. x ph -> E. x ps ) )
4 2 3 sylibr 
 |-  ( ( E. x ph -> E. x ps ) -> E. x ( ph -> ps ) )