Theorem bi123imp0

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

	Ref	Expression
Hypothesis	bi23imp0.1	|- ( ph <-> ( ps <-> ( ch <-> th ) ) )
Assertion	bi123imp0	|- ( ( ph /\ ps /\ ch ) -> th )

Proof

Step	Hyp	Ref	Expression
1		bi23imp0.1	|- ( ph <-> ( ps <-> ( ch <-> th ) ) )
2		biimp	|- ( ( ps <-> ( ch <-> th ) ) -> ( ps -> ( ch <-> th ) ) )
3		biimp	|- ( ( ch <-> th ) -> ( ch -> th ) )
4	2 3	syl6	|- ( ( ps <-> ( ch <-> th ) ) -> ( ps -> ( ch -> th ) ) )
5	1 4	sylbi	|- ( ph -> ( ps -> ( ch -> th ) ) )
6	5	3imp	|- ( ( ph /\ ps /\ ch ) -> th )