Theorem nom10 299

Description: Part of Lemma 3.3(14) from "Non-Orthomodular Models..." paper.

Assertion

Ref	Expression
nom10	(a →0 (a ∩ b)) = (a →1 b)

Proof of Theorem nom10

Step	Hyp	Ref	Expression
1		id 58	. 2 (a⊥ ∪ (a ∩ b)) = (a⊥ ∪ (a ∩ b))
2		df-i0 42	. 2 (a →0 (a ∩ b)) = (a⊥ ∪ (a ∩ b))
3		df-i1 43	. 2 (a →1 b) = (a⊥ ∪ (a ∩ b))
4	1, 2, 3	3tr1 60	1 (a →0 (a ∩ b)) = (a →1 b)

Syntax hints:   = wb 1  ^⊥ wn 4   ∪ wo 6   ∩ wa 7   →₀ wi0 12   →₁ wi1 13

This theorem is referenced by:  nom40 317

This theorem was proved from axioms:  ax-a1 29  ax-r1 34  ax-r2 35

This theorem depends on definitions:  df-i0 42  df-i1 43

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