Theorem nom60 329

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

Assertion

Ref	Expression
nom60	(b ==0 (a v b)) = (a ->2 b)

Proof of Theorem nom60

Step	Hyp	Ref	Expression
1		ancom 68	. . 3 ((b_|_ v (a v b)) ^ ((a v b)_|_ v b)) = (((a v b)_|_ v b) ^ (b_|_ v (a v b)))
2		df-id0 48	. . 3 (b ==0 (a v b)) = ((b_|_ v (a v b)) ^ ((a v b)_|_ v b))
3		df-id0 48	. . 3 ((a v b) ==0 b) = (((a v b)_|_ v b) ^ (b_|_ v (a v b)))
4	1, 2, 3	3tr1 60	. 2 (b ==0 (a v b)) = ((a v b) ==0 b)
5		nom50 323	. 2 ((a v b) ==0 b) = (a ->2 b)
6	4, 5	ax-r2 35	1 (b ==0 (a v b)) = (a ->2 b)

Syntax hints:   = wb 1  _|_wn 4   v wo 6   ^ wa 7   ->2 wi2 14   ==0 wid0 18

This theorem was proved from axioms:  ax-a1 29  ax-a2 30  ax-a3 31  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-f 41  df-i1 43  df-i2 44  df-id0 48  df-le1 122  df-le2 123

metamath.org