Theorem nom43 320

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

Assertion

Ref	Expression
nom43	((a v b) ->3 b) = (a ->2 b)

Proof of Theorem nom43

Step	Hyp	Ref	Expression
1		ancom 68	. . . . . 6 (b_|_ ^ a_|_) = (a_|_ ^ b_|_)
2		anor3 82	. . . . . 6 (a_|_ ^ b_|_) = (a v b)_|_
3	1, 2	ax-r2 35	. . . . 5 (b_|_ ^ a_|_) = (a v b)_|_
4	3	ud4lem0a 254	. . . 4 (b_|_ ->4 (b_|_ ^ a_|_)) = (b_|_ ->4 (a v b)_|_)
5	4	ax-r1 34	. . 3 (b_|_ ->4 (a v b)_|_) = (b_|_ ->4 (b_|_ ^ a_|_))
6		nom14 303	. . 3 (b_|_ ->4 (b_|_ ^ a_|_)) = (b_|_ ->1 a_|_)
7	5, 6	ax-r2 35	. 2 (b_|_ ->4 (a v b)_|_) = (b_|_ ->1 a_|_)
8		i3i4 262	. 2 ((a v b) ->3 b) = (b_|_ ->4 (a v b)_|_)
9		i2i1 259	. 2 (a ->2 b) = (b_|_ ->1 a_|_)
10	7, 8, 9	3tr1 60	1 ((a v b) ->3 b) = (a ->2 b)

Syntax hints:   = wb 1  _|_wn 4   v wo 6   ^ wa 7   ->1 wi1 13   ->2 wi2 14   ->3 wi3 15   ->4 wi4 16

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-i3 45  df-i4 46  df-le1 122  df-le2 123

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