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Theorem u3lem9 784
 Description: Lemma for unified implication study.
Assertion
Ref Expression
u3lem9 (a3 (a3 (a3 b))) = (a3 (a3 b))

Proof of Theorem u3lem9
StepHypRef Expression
1 comi31 508 . . 3 a C (a3 (a3 b))
21u3lemc4 703 . 2 (a3 (a3 (a3 b))) = (a ∪ (a3 (a3 b)))
3 u3lem7 774 . . . 4 (a3 (a3 b)) = (a ∪ ((ab) ∪ (ab )))
43lor 70 . . 3 (a ∪ (a3 (a3 b))) = (a ∪ (a ∪ ((ab) ∪ (ab ))))
5 ax-a3 32 . . . . 5 ((aa ) ∪ ((ab) ∪ (ab ))) = (a ∪ (a ∪ ((ab) ∪ (ab ))))
65ax-r1 35 . . . 4 (a ∪ (a ∪ ((ab) ∪ (ab )))) = ((aa ) ∪ ((ab) ∪ (ab )))
7 oridm 110 . . . . . 6 (aa ) = a
87ax-r5 38 . . . . 5 ((aa ) ∪ ((ab) ∪ (ab ))) = (a ∪ ((ab) ∪ (ab )))
93ax-r1 35 . . . . 5 (a ∪ ((ab) ∪ (ab ))) = (a3 (a3 b))
108, 9ax-r2 36 . . . 4 ((aa ) ∪ ((ab) ∪ (ab ))) = (a3 (a3 b))
116, 10ax-r2 36 . . 3 (a ∪ (a ∪ ((ab) ∪ (ab )))) = (a3 (a3 b))
124, 11ax-r2 36 . 2 (a ∪ (a3 (a3 b))) = (a3 (a3 b))
132, 12ax-r2 36 1 (a3 (a3 (a3 b))) = (a3 (a3 b))
 Colors of variables: term Syntax hints:   = wb 1  ⊥ wn 4   ∪ wo 6   ∩ wa 7   →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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