Theorem nomcon3 304

Description: Lemma for "Non-Orthomodular Models..." paper. (Contributed by NM, 7-Feb-1999.)

Assertion

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

Proof of Theorem nomcon3

Step	Hyp	Ref	Expression
1		nomcon2 303	. 2 (b ≡2 a) = (a⊥ ≡1 b⊥ )
2		nomb32 300	. 2 (a ≡3 b) = (b ≡2 a)
3		nomb41 299	. 2 (b⊥ ≡4 a⊥ ) = (a⊥ ≡1 b⊥ )
4	1, 2, 3	3tr1 63	1 (a ≡3 b) = (b⊥ ≡4 a⊥ )

Syntax hints:   = wb 1  ^⊥ wn 4   ≡₁ wid1 18   ≡₂ wid2 19   ≡₃ wid3 20   ≡₄ wid4 21

This theorem was proved from axioms:  ax-a1 30  ax-a2 31  ax-r1 35  ax-r2 36  ax-r4 37  ax-r5 38

This theorem depends on definitions:  df-a 40  df-id1 50  df-id2 51  df-id3 52  df-id4 53

This theorem is referenced by:  nom53  334