Theorem bi123impia 38695

Description: 3impia 1261 with the implications of the hypothesis biconditionals. (Contributed by Alan Sare, 6-Nov-2017.)

Hypothesis

Ref	Expression
bi123impia.1	|- ( ( ph /\ ps ) <-> ( ch <-> th ) )

Assertion

Ref	Expression
bi123impia	|- ( ( ph /\ ps /\ ch ) -> th )

Proof of Theorem bi123impia

Step	Hyp	Ref	Expression
1		bi123impia.1	. . 3 |- ( ( ph /\ ps ) <-> ( ch <-> th ) )
2	1	biimpi 206	. 2 |- ( ( ph /\ ps ) -> ( ch <-> th ) )
3	2	biimp3a 1432	1 |- ( ( ph /\ ps /\ ch ) -> th )

Syntax hints:   -> wi 4   <-> wb 196   /\ wa 384   /\ 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)