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Metamath Proof Explorer

Theorem 19.36

Description: Theorem 19.36 of Margaris p. 90. See 19.36v for a version requiring fewer axioms. (Contributed by NM, 24-Jun-1993)

Ref Expression
Hypothesis 19.36.1 
|- F/ x ps
Assertion 19.36 
|- ( E. x ( ph -> ps ) <-> ( A. x ph -> ps ) )

Proof

Step Hyp Ref Expression
1 19.36.1 
 |-  F/ x ps
2 19.35 
 |-  ( E. x ( ph -> ps ) <-> ( A. x ph -> E. x ps ) )
3 1 19.9 
 |-  ( E. x ps <-> ps )
4 3 imbi2i 
 |-  ( ( A. x ph -> E. x ps ) <-> ( A. x ph -> ps ) )
5 2 4 bitri 
 |-  ( E. x ( ph -> ps ) <-> ( A. x ph -> ps ) )