Theorem anandi 392

Description: Distribution of conjunction over conjunction.

Assertion

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

Proof of Theorem anandi

Step	Hyp	Ref	Expression
1		anidm 331	. . 3 |- ((ph /\ ph) <-> ph)
2	1	anbi1i 368	. 2 |- (((ph /\ ph) /\ (ps /\ ch)) <-> (ph /\ (ps /\ ch)))
3		an4 388	. 2 |- (((ph /\ ph) /\ (ps /\ ch)) <-> ((ph /\ ps) /\ (ph /\ ch)))
4	2, 3	bitr3 153	1 |- ((ph /\ (ps /\ ch)) <-> ((ph /\ ps) /\ (ph /\ ch)))

Syntax hints:   <-> wb 127   /\ wa 196

This theorem is referenced by:  rnlem 579  mopick2 1057  r19.29 1295  uniin 1935  ndmoprdistr 3063  oaord 3149  nnmord 3189  isfinite1 3425  distrlem1pr 3921  addcanpr 3946

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6

This theorem depends on definitions:  df-bi 128  df-an 198

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