Theorem anandi3r 899

Description: Distribution of triple conjunction over conjunction. (Contributed by David A. Wheeler, 4-Nov-2018.)

Assertion

Ref	Expression
anandi3r	|- ( ( ph /\ ps /\ ch ) <-> ( ( ph /\ ps ) /\ ( ch /\ ps ) ) )

Proof of Theorem anandi3r

Step	Hyp	Ref	Expression
1		3anan32 896	. 2 |- ( ( ph /\ ps /\ ch ) <-> ( ( ph /\ ch ) /\ ps ) )
2		anandir 525	. 2 |- ( ( ( ph /\ ch ) /\ ps ) <-> ( ( ph /\ ps ) /\ ( ch /\ ps ) ) )
3	1, 2	bitri 173	1 |- ( ( ph /\ ps /\ ch ) <-> ( ( ph /\ ps ) /\ ( ch /\ ps ) ) )

Syntax hints:   /\ wa 97   <-> wb 98   /\ w3a 885

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101

This theorem depends on definitions:  df-bi 110  df-3an 887

This theorem is referenced by: (None)