Metamath Proof Explorer

Theorem bi23imp1

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

Ref Expression
Hypothesis bi23imp1.1 
|- ( ph -> ( ps <-> ( ch <-> th ) ) )
Assertion bi23imp1 
|- ( ( ph /\ ps /\ ch ) -> th )

Proof

Step Hyp Ref Expression
1 bi23imp1.1 
 |-  ( ph -> ( ps <-> ( ch <-> th ) ) )
2 biimp 
 |-  ( ( ch <-> th ) -> ( ch -> th ) )
3 1 2 syl6bi 
 |-  ( ph -> ( ps -> ( ch -> th ) ) )
4 3 3imp 
 |-  ( ( ph /\ ps /\ ch ) -> th )