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Theorem lem3.4.4 1077
Description: Equation 3.12 of [PavMeg1999] p. 9. (Contributed by Roy F. Longton, 29-Jun-2005.) (Revised by Roy F. Longton, 3-Jul-2005.)
Hypotheses
Ref Expression
lem3.4.4.1 (a2 b) = 1
lem3.4.4.2 (b2 a) = 1
Assertion
Ref Expression
lem3.4.4 (a5 b) = 1

Proof of Theorem lem3.4.4
StepHypRef Expression
1 lem3.4.4.2 . . . 4 (b2 a) = 1
21lem3.3.4 1053 . . 3 (a2 (a5 b)) = (a5 b)
32ax-r1 35 . 2 (a5 b) = (a2 (a5 b))
4 lem3.4.4.1 . . 3 (a2 b) = 1
54lem3.4.3 1076 . 2 (a2 (a5 b)) = 1
63, 5ax-r2 36 1 (a5 b) = 1
Colors of variables: term
Syntax hints:   = wb 1  1wt 8  2 wi2 13  5 wid5 22
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-wom 361
This theorem depends on definitions:  df-a 40  df-t 41  df-f 42  df-i1 44  df-i2 45  df-le1 130  df-le2 131  df-id5 1047
This theorem is referenced by:  lem3.4.6  1079
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