Theorem wanass 196

Description: Associative law.

Assertion

Ref	Expression
wanass	(((a ∩ b) ∩ c) ≡ (a ∩ (b ∩ c))) = 1

Proof of Theorem wanass

Step	Hyp	Ref	Expression
1		anass 69	. 2 ((a ∩ b) ∩ c) = (a ∩ (b ∩ c))
2	1	bi1 110	1 (((a ∩ b) ∩ c) ≡ (a ∩ (b ∩ c))) = 1

Syntax hints:   = wb 1   ≡ tb 5   ∩ wa 7  1wt 9

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-b 38  df-a 39  df-t 40  df-f 41

metamath.org