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Metamath Proof Explorer

Theorem imbi2i

Description: Introduce an antecedent to both sides of a logical equivalence. This and the next three rules are useful for building up wff's around a definition, in order to make use of the definition. (Contributed by NM, 3-Jan-1993) (Proof shortened by Wolf Lammen, 6-Feb-2013)

Ref Expression
Hypothesis imbi2i.1 
|- ( ph <-> ps )
Assertion imbi2i 
|- ( ( ch -> ph ) <-> ( ch -> ps ) )

Proof

Step Hyp Ref Expression
1 imbi2i.1 
 |-  ( ph <-> ps )
2 1 a1i 
 |-  ( ch -> ( ph <-> ps ) )
3 2 pm5.74i 
 |-  ( ( ch -> ph ) <-> ( ch -> ps ) )