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Metamath Proof Explorer

Theorem pm5.21nii

Description: Eliminate an antecedent implied by each side of a biconditional. (Contributed by NM, 21-May-1999)

Ref Expression
Hypotheses pm5.21ni.1 
|- ( ph -> ps )
pm5.21ni.2 
|- ( ch -> ps )
pm5.21nii.3 
|- ( ps -> ( ph <-> ch ) )
Assertion pm5.21nii 
|- ( ph <-> ch )

Proof

Step Hyp Ref Expression
1 pm5.21ni.1 
 |-  ( ph -> ps )
2 pm5.21ni.2 
 |-  ( ch -> ps )
3 pm5.21nii.3 
 |-  ( ps -> ( ph <-> ch ) )
4 1 2 pm5.21ni 
 |-  ( -. ps -> ( ph <-> ch ) )
5 3 4 pm2.61i 
 |-  ( ph <-> ch )