Theorem nom32 321

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

Assertion

Ref	Expression
nom32	((a ∩ b) ≡2 a) = (a →1 b)

Proof of Theorem nom32

Step	Hyp	Ref	Expression
1		nomb32 300	. . 3 (a ≡3 (a ∩ b)) = ((a ∩ b) ≡2 a)
2	1	ax-r1 35	. 2 ((a ∩ b) ≡2 a) = (a ≡3 (a ∩ b))
3		nom23 316	. 2 (a ≡3 (a ∩ b)) = (a →1 b)
4	2, 3	ax-r2 36	1 ((a ∩ b) ≡2 a) = (a →1 b)

Syntax hints:   = wb 1   ∩ wa 7   →₁ wi1 12   ≡₂ wid2 19   ≡₃ wid3 20

This theorem was proved from axioms:  ax-a1 30  ax-a2 31  ax-a4 33  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-i1 44  df-id2 51  df-id3 52  df-le1 130  df-le2 131

This theorem is referenced by: (None)