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Theorem i3th6 548
 Description: Theorem for Kalmbach implication. (Contributed by NM, 16-Nov-1997.)
Assertion
Ref Expression
i3th6 ((a3 (a3 (a3 b))) →3 (a3 (a3 b))) = 1

Proof of Theorem i3th6
StepHypRef Expression
1 i3abs1 522 . . 3 (a3 (a3 (a3 b))) = (a3 (a3 b))
21bi1 118 . 2 ((a3 (a3 (a3 b))) ≡ (a3 (a3 b))) = 1
3 bii3 516 . 2 (((a3 (a3 (a3 b))) ≡ (a3 (a3 b))) →3 ((a3 (a3 (a3 b))) →3 (a3 (a3 b)))) = 1
42, 3skmp3 245 1 ((a3 (a3 (a3 b))) →3 (a3 (a3 b))) = 1
 Colors of variables: term Syntax hints:   = wb 1   ≡ tb 5  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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