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Theorem i3i0 513
Description: Translation from Kalmbach implication. (Contributed by NM, 9-Nov-1997.)
Hypothesis
Ref Expression
i3i0.1 (a3 (a3 b)) = 1
Assertion
Ref Expression
i3i0 (ab) = 1

Proof of Theorem i3i0
StepHypRef Expression
1 lem4 511 . . 3 (a3 (a3 b)) = (ab)
21ax-r1 35 . 2 (ab) = (a3 (a3 b))
3 i3i0.1 . 2 (a3 (a3 b)) = 1
42, 3ax-r2 36 1 (ab) = 1
Colors of variables: term
Syntax hints:   = wb 1   wn 4  wo 6  1wt 8  3 wi3 14
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-i3 46  df-le1 130  df-le2 131  df-c1 132  df-c2 133
This theorem is referenced by:  i0i3tr  541  i3i0tr  542
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