Theorem bi12imp3 38700

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

Hypothesis

Ref	Expression
bi12imp3.1	|- ( ph <-> ( ps <-> ( ch -> th ) ) )

Assertion

Ref	Expression
bi12imp3	|- ( ( ph /\ ps /\ ch ) -> th )

Proof of Theorem bi12imp3

Step	Hyp	Ref	Expression
1		bi12imp3.1	. . 3 |- ( ph <-> ( ps <-> ( ch -> th ) ) )
2	1	biimpi 206	. 2 |- ( ph -> ( ps <-> ( ch -> th ) ) )
3	2	bi23imp13 38697	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)