Metamath Proof Explorer

Theorem bi12imp3

Description: Similar to 3imp except all but innermost implication are biconditionals. (Contributed by Alan Sare, 6-Nov-2017)

Ref Expression
Hypothesis bi12imp3.1 
|- ( ph <-> ( ps <-> ( ch -> th ) ) )
Assertion bi12imp3 
|- ( ( ph /\ ps /\ ch ) -> th )

Proof

Step Hyp Ref Expression
1 bi12imp3.1 
 |-  ( ph <-> ( ps <-> ( ch -> th ) ) )
2 1 biimpi 
 |-  ( ph -> ( ps <-> ( ch -> th ) ) )
3 2 bi23imp13 
 |-  ( ( ph /\ ps /\ ch ) -> th )