Theorem biid 108

Description: Identity law.

Assertion

Ref	Expression
biid	(a ≡ a) = 1

Proof of Theorem biid

Step	Hyp	Ref	Expression
1		anidm 103	. . 3 (a ∩ a) = a
2		anidm 103	. . 3 (a⊥ ∩ a⊥ ) = a⊥
3	1, 2	2or 67	. 2 ((a ∩ a) ∪ (a⊥ ∩ a⊥ )) = (a ∪ a⊥ )
4		dfb 86	. 2 (a ≡ a) = ((a ∩ a) ∪ (a⊥ ∩ a⊥ ))
5		df-t 40	. 2 1 = (a ∪ a⊥ )
6	3, 4, 5	3tr1 60	1 (a ≡ a) = 1

Syntax hints:   = wb 1  ^⊥ wn 4   ≡ tb 5   ∪ wo 6   ∩ wa 7  1wt 9

This theorem is referenced by:  bi1 110  ska1 223

This theorem was proved from axioms:  ax-a1 29  ax-a2 30  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

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