Theorem nom55 328

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

Assertion

Ref	Expression
nom55	((a v b) == b) = (a ->2 b)

Proof of Theorem nom55

Step	Hyp	Ref	Expression
1		nom25 310	. 2 (b_|_ == (b_|_ ^ a_|_)) = (b_|_ ->1 a_|_)
2		conb 114	. . 3 ((a v b) == b) = ((a v b)_|_ == b_|_)
3		bicom 88	. . 3 ((a v b)_|_ == b_|_) = (b_|_ == (a v b)_|_)
4		ancom 68	. . . . . 6 (b_|_ ^ a_|_) = (a_|_ ^ b_|_)
5		anor3 82	. . . . . 6 (a_|_ ^ b_|_) = (a v b)_|_
6	4, 5	ax-r2 35	. . . . 5 (b_|_ ^ a_|_) = (a v b)_|_
7	6	ax-r1 34	. . . 4 (a v b)_|_ = (b_|_ ^ a_|_)
8	7	lbi 89	. . 3 (b_|_ == (a v b)_|_) = (b_|_ == (b_|_ ^ a_|_))
9	2, 3, 8	3tr 62	. 2 ((a v b) == b) = (b_|_ == (b_|_ ^ a_|_))
10		i2i1 259	. 2 (a ->2 b) = (b_|_ ->1 a_|_)
11	1, 9, 10	3tr1 60	1 ((a v b) == b) = (a ->2 b)

Syntax hints:   = wb 1  _|_wn 4   == tb 5   v wo 6   ^ wa 7   ->1 wi1 13   ->2 wi2 14

This theorem is referenced by:  nom65 334

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-b 38  df-a 39  df-t 40  df-f 41  df-i1 43  df-i2 44

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