Theorem nom61 330

Description: Part of Lemma 3.3(15) from "Non-Orthomodular Models..." paper.

Assertion

Ref	Expression
nom61	(b ≡1 (a ∪ b)) = (a →2 b)

Proof of Theorem nom61

Step	Hyp	Ref	Expression
1		nomb41 291	. . 3 ((a ∪ b) ≡4 b) = (b ≡1 (a ∪ b))
2	1	ax-r1 34	. 2 (b ≡1 (a ∪ b)) = ((a ∪ b) ≡4 b)
3		nom54 327	. 2 ((a ∪ b) ≡4 b) = (a →2 b)
4	2, 3	ax-r2 35	1 (b ≡1 (a ∪ b)) = (a →2 b)

Syntax hints:   = wb 1   ∪ wo 6   →₂ wi2 14   ≡₁ wid1 19   ≡₄ wid4 22

This theorem was proved from axioms:  ax-a1 29  ax-a2 30  ax-a4 32  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-i1 43  df-i2 44  df-id1 49  df-id2 50  df-id3 51  df-id4 52  df-le1 122  df-le2 123

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