Theorem anandi 801

Description: Distribution of conjunction over conjunction. (Contributed by NM, 14-Aug-1995.)

Assertion

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

Proof of Theorem anandi

Step	Hyp	Ref	Expression
1		anidm 625	. . 3 |- ((ph /\ ph) <-> ph)
2	1	anbi1i 676	. 2 |- (((ph /\ ph) /\ (ps /\ ch)) <-> (ph /\ (ps /\ ch)))
3		an4 797	. 2 |- (((ph /\ ph) /\ (ps /\ ch)) <-> ((ph /\ ps) /\ (ph /\ ch)))
4	2, 3	bitr3i 242	1 |- ((ph /\ (ps /\ ch)) <-> ((ph /\ ps) /\ (ph /\ ch)))

Syntax hints:   <-> wb 176   /\ wa 358

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 177  df-an 360

This theorem is referenced by:  inrab  3528  uniin  3912  fin  5247  inpreima  5410  fununiq  5518  ndmovdistr  5620  trtxp  5782