Theorem nom62 339

Description: Part of Lemma 3.3(15) from "Non-Orthomodular Models..." paper. (Contributed by NM, 7-Feb-1999.)

Assertion

Ref	Expression
nom62	(b ≡2 (a ∪ b)) = (a →2 b)

Proof of Theorem nom62

Step	Hyp	Ref	Expression
1		nomb32 300	. . 3 ((a ∪ b) ≡3 b) = (b ≡2 (a ∪ b))
2	1	ax-r1 35	. 2 (b ≡2 (a ∪ b)) = ((a ∪ b) ≡3 b)
3		nom53 334	. 2 ((a ∪ b) ≡3 b) = (a →2 b)
4	2, 3	ax-r2 36	1 (b ≡2 (a ∪ b)) = (a →2 b)

Syntax hints:   = wb 1   ∪ wo 6   →₂ wi2 13   ≡₂ wid2 19   ≡₃ wid3 20

This theorem was proved from axioms:  ax-a1 30  ax-a2 31  ax-a3 32  ax-a5 34  ax-r1 35  ax-r2 36  ax-r4 37  ax-r5 38

This theorem depends on definitions:  df-a 40  df-t 41  df-f 42  df-i1 44  df-i2 45  df-id1 50  df-id2 51  df-id3 52  df-id4 53  df-le1 130  df-le2 131

This theorem is referenced by: (None)