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Theorem i3i0tr 542
 Description: Transitive inference.
Hypotheses
Ref Expression
i3i0tr.1 (a3 b) = 1
i3i0tr.2 (b3 (b3 c)) = 1
Assertion
Ref Expression
i3i0tr (a3 (a3 c)) = 1

Proof of Theorem i3i0tr
StepHypRef Expression
1 i3i0tr.2 . . . 4 (b3 (b3 c)) = 1
21i3i0 513 . . 3 (bc) = 1
3 i3i0tr.1 . . . . 5 (a3 b) = 1
43binr1 517 . . . 4 (b3 a ) = 1
54i3ror 532 . . 3 ((bc) →3 (ac)) = 1
62, 5skmp3 245 . 2 (ac) = 1
76i0i3 512 1 (a3 (a3 c)) = 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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