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Theorem u3lem2 746
 Description: Lemma for unified implication study.
Assertion
Ref Expression
u3lem2 (((a3 b) →3 a) →3 a) = (a ∪ ((ab) ∪ (ab )))

Proof of Theorem u3lem2
StepHypRef Expression
1 comi31 508 . . . . 5 a C (a3 b)
2 comid 187 . . . . 5 a C a
31, 2u3lemc2 688 . . . 4 a C ((a3 b) →3 a)
43comcom 453 . . 3 ((a3 b) →3 a) C a
54u3lemc4 703 . 2 (((a3 b) →3 a) →3 a) = (((a3 b) →3 a)a)
6 u3lem1n 741 . . . 4 ((a3 b) →3 a) = ((ab) ∪ (ab ))
76ax-r5 38 . . 3 (((a3 b) →3 a)a) = (((ab) ∪ (ab )) ∪ a)
8 ax-a2 31 . . 3 (((ab) ∪ (ab )) ∪ a) = (a ∪ ((ab) ∪ (ab )))
97, 8ax-r2 36 . 2 (((a3 b) →3 a)a) = (a ∪ ((ab) ∪ (ab )))
105, 9ax-r2 36 1 (((a3 b) →3 a) →3 a) = (a ∪ ((ab) ∪ (ab )))
 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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