Theorem nomcon3 296

Description: Lemma for "Non-Orthomodular Models..." paper.

Assertion

Ref	Expression
nomcon3	(a ≡3 b) = (b⊥ ≡4 a⊥ )

Proof of Theorem nomcon3

Step	Hyp	Ref	Expression
1		nomcon2 295	. 2 (b ≡2 a) = (a⊥ ≡1 b⊥ )
2		nomb32 292	. 2 (a ≡3 b) = (b ≡2 a)
3		nomb41 291	. 2 (b⊥ ≡4 a⊥ ) = (a⊥ ≡1 b⊥ )
4	1, 2, 3	3tr1 60	1 (a ≡3 b) = (b⊥ ≡4 a⊥ )

Syntax hints:   = wb 1  ^⊥ wn 4   ≡₁ wid1 19   ≡₂ wid2 20   ≡₃ wid3 21   ≡₄ wid4 22

This theorem is referenced by:  nom53 326

This theorem was proved from axioms:  ax-a1 29  ax-a2 30  ax-r1 34  ax-r2 35  ax-r4 36  ax-r5 37

This theorem depends on definitions:  df-a 39  df-id1 49  df-id2 50  df-id3 51  df-id4 52

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