Theorem anandir 393

Description: Distribution of conjunction over conjunction.

Assertion

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

Proof of Theorem anandir

Step	Hyp	Ref	Expression
1		anidm 331	. . 3 |- ((ch /\ ch) <-> ch)
2	1	anbi2i 367	. 2 |- (((ph /\ ps) /\ (ch /\ ch)) <-> ((ph /\ ps) /\ ch))
3		an4 388	. 2 |- (((ph /\ ps) /\ (ch /\ ch)) <-> ((ph /\ ch) /\ (ps /\ ch)))
4	2, 3	bitr3 153	1 |- (((ph /\ ps) /\ ch) <-> ((ph /\ ch) /\ (ps /\ ch)))

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

This theorem is referenced by:  rnlem 579  fununi 2705  imadif 2714  axrecex 4079  nnleltp1t 4448  5oalem3 5546  5oalem5 5548

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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