Theorem bi23imp1 38701

Description: Similar to 3imp 1256 except all but outermost implication are biconditionals. (Contributed by Alan Sare, 6-Nov-2017.)

Hypothesis

Ref	Expression
bi23imp1.1	|- ( ph -> ( ps <-> ( ch <-> th ) ) )

Assertion

Ref	Expression
bi23imp1	|- ( ( ph /\ ps /\ ch ) -> th )

Proof of Theorem bi23imp1

Step	Hyp	Ref	Expression
1		bi23imp1.1	. . 3 |- ( ph -> ( ps <-> ( ch <-> th ) ) )
2		biimp 205	. . 3 |- ( ( ch <-> th ) -> ( ch -> th ) )
3	1, 2	syl6bi 243	. 2 |- ( ph -> ( ps -> ( ch -> th ) ) )
4	3	3imp 1256	1 |- ( ( ph /\ ps /\ ch ) -> th )

Syntax hints:   -> wi 4   <-> wb 196   /\ w3a 1037

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 197  df-an 386  df-3an 1039

This theorem is referenced by: (None)