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Theorem oa3-5lem 984

Description: Lemma for 3-OA(5). Equivalence with substitution into 6-OA dual.

Assertion

Ref	Expression
oa3-5lem

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Proof of Theorem oa3-5lem

Step	Hyp	Ref	Expression
1		or12 80	. . . . . . 7
2		oridm 110	. . . . . . . 8
3	2	lor 70	. . . . . . 7
4	1, 3	ax-r2 36	. . . . . 6
5		an1 106	. . . . . . . 8
6		df-i1 44	. . . . . . . 8
7	5, 6	ax-r2 36	. . . . . . 7
8	7	lor 70	. . . . . 6
9	4, 8, 6	3tr1 63	. . . . 5
10		or12 80	. . . . . . . . 9
11		ancom 74	. . . . . . . . . . . 12
12	11	ax-r5 38	. . . . . . . . . . 11
13		oridm 110	. . . . . . . . . . 11
14	12, 13	ax-r2 36	. . . . . . . . . 10
15	14	lor 70	. . . . . . . . 9
16	10, 15	ax-r2 36	. . . . . . . 8
17		ancom 74	. . . . . . . . . 10
18		an1 106	. . . . . . . . . 10
19		df-i1 44	. . . . . . . . . 10
20	17, 18, 19	3tr 65	. . . . . . . . 9
21	20	lor 70	. . . . . . . 8
22	16, 21, 19	3tr1 63	. . . . . . 7
23	22	lan 77	. . . . . 6
24		ancom 74	. . . . . 6
25	23, 24	ax-r2 36	. . . . 5
26	9, 25	2or 72	. . . 4
27	26	lan 77	. . 3
28	27	lor 70	. 2
29	28	lan 77	1

Colors of variables: term

Syntax hints:   wb 1  wn 4   wo 6   wa 7  wt 8   wi1 12

This theorem was proved from axioms:  ax-a1 30  ax-a2 31  ax-a3 32  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-f 42  df-i1 44

This theorem is referenced by: (None)

Copyright terms: Public domain

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