Theorem anandi3 932

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

Assertion

Ref	Expression
anandi3	|- ( ( ph /\ ps /\ ch ) <-> ( ( ph /\ ps ) /\ ( ph /\ ch ) ) )

Proof of Theorem anandi3

Step	Hyp	Ref	Expression
1		3anass 923	. 2 |- ( ( ph /\ ps /\ ch ) <-> ( ph /\ ( ps /\ ch ) ) )
2		anandi 554	. 2 |- ( ( ph /\ ( ps /\ ch ) ) <-> ( ( ph /\ ps ) /\ ( ph /\ ch ) ) )
3	1, 2	bitri 182	1 |- ( ( ph /\ ps /\ ch ) <-> ( ( ph /\ ps ) /\ ( ph /\ ch ) ) )

Syntax hints:   /\ wa 102   <-> wb 103   /\ w3a 919

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106

This theorem depends on definitions:  df-bi 115  df-3an 921

This theorem is referenced by: (None)