Theorem nom10 307

Description: Part of Lemma 3.3(14) from "Non-Orthomodular Models..." paper. (Contributed by NM, 7-Feb-1999.)

Assertion

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

Proof of Theorem nom10

Step	Hyp	Ref	Expression
1		id 59	. 2 (a⊥ ∪ (a ∩ b)) = (a⊥ ∪ (a ∩ b))
2		df-i0 43	. 2 (a →0 (a ∩ b)) = (a⊥ ∪ (a ∩ b))
3		df-i1 44	. 2 (a →1 b) = (a⊥ ∪ (a ∩ b))
4	1, 2, 3	3tr1 63	1 (a →0 (a ∩ b)) = (a →1 b)

Syntax hints:   = wb 1  ^⊥ wn 4   ∪ wo 6   ∩ wa 7   →₀ wi0 11   →₁ wi1 12

This theorem was proved from axioms:  ax-a1 30  ax-r1 35  ax-r2 36

This theorem depends on definitions:  df-i0 43  df-i1 44

This theorem is referenced by:  nom40  325  lem3.3.7i0e3  1059