Metamath Proof Explorer

Theorem bi13imp23

Description: 3imp with outermost implication of the hypothesis a biconditional. (Contributed by Alan Sare, 6-Nov-2017)

Ref Expression
Hypothesis bi13imp23.1 
|- ( ph <-> ( ps -> ( ch -> th ) ) )
Assertion bi13imp23 
|- ( ( ph /\ ps /\ ch ) -> th )

Proof

Step Hyp Ref Expression
1 bi13imp23.1 
 |-  ( ph <-> ( ps -> ( ch -> th ) ) )
2 1 biimpi 
 |-  ( ph -> ( ps -> ( ch -> th ) ) )
3 2 3imp 
 |-  ( ( ph /\ ps /\ ch ) -> th )