Theorem omlem2 120

Description: Lemma in proof of Th. 1 of Pavicic 1987.

Assertion

Ref	Expression
omlem2	((a v b)_|_ v (a v (a_|_ ^ (a v b)))) = 1

Proof of Theorem omlem2

Step	Hyp	Ref	Expression
1		ax-a2 30	. . 3 ((a v b)_|_ v a) = (a v (a v b)_|_)
2		anor2 81	. . 3 (a_|_ ^ (a v b)) = (a v (a v b)_|_)_|_
3	1, 2	2or 67	. 2 (((a v b)_|_ v a) v (a_|_ ^ (a v b))) = ((a v (a v b)_|_) v (a v (a v b)_|_)_|_)
4		ax-a3 31	. . 3 (((a v b)_|_ v a) v (a_|_ ^ (a v b))) = ((a v b)_|_ v (a v (a_|_ ^ (a v b))))
5	4	ax-r1 34	. 2 ((a v b)_|_ v (a v (a_|_ ^ (a v b)))) = (((a v b)_|_ v a) v (a_|_ ^ (a v b)))
6		df-t 40	. 2 1 = ((a v (a v b)_|_) v (a v (a v b)_|_)_|_)
7	3, 5, 6	3tr1 60	1 ((a v b)_|_ v (a v (a_|_ ^ (a v b)))) = 1

Syntax hints:   = wb 1  _|_wn 4   v wo 6   ^ wa 7  1wt 9

This theorem is referenced by:  woml 203  wql2lem3 282  oml 427

This theorem was proved from axioms:  ax-a1 29  ax-a2 30  ax-a3 31  ax-r1 34  ax-r2 35  ax-r4 36  ax-r5 37

This theorem depends on definitions:  df-a 39  df-t 40

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