Theorem anandi 106

Description: Distribution of conjunction over conjunction.

Assertion

Ref	Expression
anandi	(a ∩ (b ∩ c)) = ((a ∩ b) ∩ (a ∩ c))

Proof of Theorem anandi

Step	Hyp	Ref	Expression
1		anidm 103	. . . 4 (a ∩ a) = a
2	1	ax-r1 34	. . 3 a = (a ∩ a)
3	2	ran 71	. 2 (a ∩ (b ∩ c)) = ((a ∩ a) ∩ (b ∩ c))
4		an4 78	. 2 ((a ∩ a) ∩ (b ∩ c)) = ((a ∩ b) ∩ (a ∩ c))
5	3, 4	ax-r2 35	1 (a ∩ (b ∩ c)) = ((a ∩ b) ∩ (a ∩ c))

Syntax hints:   = wb 1   ∩ wa 7

This theorem is referenced by:  wwfh1 208  wdf-c2 366  wfh1 405  fh1 451  i3bi 478  u5lembi 707  u3lem13b 772  3vth9 794  mlaoml 815  comanblem1 852

This theorem was proved from axioms:  ax-a1 29  ax-a2 30  ax-a3 31  ax-a5 33  ax-r1 34  ax-r2 35  ax-r4 36  ax-r5 37

This theorem depends on definitions:  df-a 39  df-t 40  df-f 41

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