Theorem i1id 267

Description: Identity law for Sasaki conditional.

Assertion

Ref	Expression
i1id	(a →1 a) = 1

Proof of Theorem i1id

Step	Hyp	Ref	Expression
1		df-i1 43	. 2 (a →1 a) = (a⊥ ∪ (a ∩ a))
2		ax-a2 30	. . 3 (a⊥ ∪ a) = (a ∪ a⊥ )
3		anidm 103	. . . 4 (a ∩ a) = a
4	3	lor 66	. . 3 (a⊥ ∪ (a ∩ a)) = (a⊥ ∪ a)
5		df-t 40	. . 3 1 = (a ∪ a⊥ )
6	2, 4, 5	3tr1 60	. 2 (a⊥ ∪ (a ∩ a)) = 1
7	1, 6	ax-r2 35	1 (a →1 a) = 1

Syntax hints:   = wb 1  ^⊥ wn 4   ∪ wo 6   ∩ wa 7  1wt 9   →₁ wi1 13

This theorem is referenced by:  oa3-2lemb 959

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-a 39  df-t 40  df-f 41  df-i1 43

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