Theorem anandir 872

Description: Distribution of conjunction over conjunction. (Contributed by NM, 24-Aug-1995.)

Assertion

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

Proof of Theorem anandir

Step	Hyp	Ref	Expression
1		anidm 676	. . 3 |- ( ( ch /\ ch ) <-> ch )
2	1	anbi2i 730	. 2 |- ( ( ( ph /\ ps ) /\ ( ch /\ ch ) ) <-> ( ( ph /\ ps ) /\ ch ) )
3		an4 865	. 2 |- ( ( ( ph /\ ps ) /\ ( ch /\ ch ) ) <-> ( ( ph /\ ch ) /\ ( ps /\ ch ) ) )
4	2, 3	bitr3i 266	1 |- ( ( ( ph /\ ps ) /\ ch ) <-> ( ( ph /\ ch ) /\ ( ps /\ ch ) ) )

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

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

This theorem is referenced by:  anandi3r  1053  disjxun  4651  fununi  5964  imadif  5973  wfrlem5  7419  elfzuzb  12336  frgr3v  27139  5oalem3  28515  5oalem5  28517  frrlem5  31784  nzin  38517  un2122  39017