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Metamath Proof Explorer

Theorem 19.37v

Description: Version of 19.37 with a disjoint variable condition, requiring fewer axioms. (Contributed by NM, 21-Jun-1993)

Ref Expression
Assertion 19.37v 
|- ( E. x ( ph -> ps ) <-> ( ph -> E. x ps ) )

Proof

Step Hyp Ref Expression
1 19.35 
 |-  ( E. x ( ph -> ps ) <-> ( A. x ph -> E. x ps ) )
2 19.3v 
 |-  ( A. x ph <-> ph )
3 2 imbi1i 
 |-  ( ( A. x ph -> E. x ps ) <-> ( ph -> E. x ps ) )
4 1 3 bitri 
 |-  ( E. x ( ph -> ps ) <-> ( ph -> E. x ps ) )