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Theorem u1lem5 761
 Description: Lemma for unified implication study.
Assertion
Ref Expression
u1lem5 (a1 (a1 b)) = (a1 b)

Proof of Theorem u1lem5
StepHypRef Expression
1 df-i1 44 . 2 (a1 (a1 b)) = (a ∪ (a ∩ (a1 b)))
2 ancom 74 . . . . 5 (a ∩ (a1 b)) = ((a1 b) ∩ a)
3 u1lemaa 600 . . . . 5 ((a1 b) ∩ a) = (ab)
42, 3ax-r2 36 . . . 4 (a ∩ (a1 b)) = (ab)
54lor 70 . . 3 (a ∪ (a ∩ (a1 b))) = (a ∪ (ab))
6 df-i1 44 . . . 4 (a1 b) = (a ∪ (ab))
76ax-r1 35 . . 3 (a ∪ (ab)) = (a1 b)
85, 7ax-r2 36 . 2 (a ∪ (a ∩ (a1 b))) = (a1 b)
91, 8ax-r2 36 1 (a1 (a1 b)) = (a1 b)
 Colors of variables: term Syntax hints:   = wb 1  ⊥ wn 4   ∪ wo 6   ∩ wa 7   →1 wi1 12 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-i1 44  df-le1 130  df-le2 131  df-c1 132  df-c2 133 This theorem is referenced by: (None)
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