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Theorem i3th8 550
 Description: Theorem for Kalmbach implication. (Contributed by NM, 19-Nov-1997.)
Assertion
Ref Expression
i3th8 ((a3 b)3 ((a3 b) →3 a)) = 1

Proof of Theorem i3th8
StepHypRef Expression
1 leo 158 . . 3 (a3 b) ≤ ((a3 b)a)
2 lem4 511 . . . . 5 ((a3 b) →3 ((a3 b) →3 a)) = ((a3 b)a)
32ax-r1 35 . . . 4 ((a3 b)a) = ((a3 b) →3 ((a3 b) →3 a))
4 i3abs3 524 . . . 4 ((a3 b) →3 ((a3 b) →3 a)) = ((a3 b) →3 a)
53, 4ax-r2 36 . . 3 ((a3 b)a) = ((a3 b) →3 a)
61, 5lbtr 139 . 2 (a3 b) ≤ ((a3 b) →3 a)
76lei3 246 1 ((a3 b)3 ((a3 b) →3 a)) = 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: (None)
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