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Theorem govar 896

Description: Lemma for converting n-variable Godowski equations to 2n-variable equations.

Hypotheses

Ref	Expression
govar.1
govar.2

Assertion

Ref	Expression
govar

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Proof of Theorem govar

Step	Hyp	Ref	Expression
1		df-i2 45	. . . 4
2	1	lan 77	. . 3
3		ax-a2 31	. . . . 5
4	3	ran 78	. . . 4
5		govar.2	. . . . . . . 8
6	5	lecom 180	. . . . . . 7
7	6	comcom7 460	. . . . . 6
8		govar.1	. . . . . . . . . . 11
9	8	lecom 180	. . . . . . . . . 10
10	9	comcom7 460	. . . . . . . . 9
11	10	comcom 453	. . . . . . . 8
12	11	comcom2 183	. . . . . . 7
13	12, 6	com2an 484	. . . . . 6
14	7, 13	com2or 483	. . . . 5
15	14, 11	fh2r 474	. . . 4
16	4, 15	ax-r2 36	. . 3
17		coman1 185	. . . . . . 7
18	17	comcom7 460	. . . . . 6
19		coman2 186	. . . . . . 7
20	19	comcom7 460	. . . . . 6
21	18, 20	fh2c 477	. . . . 5
22		dff 101	. . . . . . . . 9
23	22	ran 78	. . . . . . . 8
24	23	ax-r1 35	. . . . . . 7
25		anass 76	. . . . . . 7
26		an0r 109	. . . . . . 7
27	24, 25, 26	3tr2 64	. . . . . 6
28	27	lor 70	. . . . 5
29		or0 102	. . . . 5
30	21, 28, 29	3tr 65	. . . 4
31	30	lor 70	. . 3
32	2, 16, 31	3tr 65	. 2
33		lea 160	. . 3
34		lear 161	. . 3
35	33, 34	le2or 168	. 2
36	32, 35	bltr 138	1

Colors of variables: term

Syntax hints:   wle 2  wn 4   wo 6   wa 7  wf 9   wi2 13

This theorem was proved from axioms:  ax-a1 30  ax-a2 31  ax-a3 32  ax-a4 33  ax-a5 34  ax-r1 35  ax-r2 36  ax-r4 37  ax-r5 38  ax-r3 439

This theorem depends on definitions:  df-b 39  df-a 40  df-t 41  df-f 42  df-i2 45  df-le1 130  df-le2 131  df-c1 132  df-c2 133

This theorem is referenced by:  gon2n  898

Copyright terms: Public domain

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