Theorem anandir 513

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 434	. . 3 |- ((ch /\ ch) <-> ch)
2	1	anbi2i 482	. 2 |- (((ph /\ ps) /\ (ch /\ ch)) <-> ((ph /\ ps) /\ ch))
3		an4 508	. 2 |- (((ph /\ ps) /\ (ch /\ ch)) <-> ((ph /\ ch) /\ (ps /\ ch)))
4	2, 3	bitr3 175	1 |- (((ph /\ ps) /\ ch) <-> ((ph /\ ch) /\ (ps /\ ch)))

Syntax hints:   <-> wb 146   /\ wa 223

This theorem is referenced by:  rnlem 775  fununi 3569  imadif 3580  nnleltp1t 5956  elfzuzb 6477  5oalem3 9596  5oalem5 9598

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7

This theorem depends on definitions:  df-bi 147  df-an 225

Copyright terms: Public domain