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Theorem ud2lem0c 278
 Description: Lemma for unified disjunction. (Contributed by NM, 23-Nov-1997.)
Assertion
Ref Expression
ud2lem0c (a2 b) = (b ∩ (ab))

Proof of Theorem ud2lem0c
StepHypRef Expression
1 df-i2 45 . . 3 (a2 b) = (b ∪ (ab ))
2 oran 87 . . . 4 (b ∪ (ab )) = (b ∩ (ab ) )
3 oran 87 . . . . . . 7 (ab) = (ab )
43ax-r1 35 . . . . . 6 (ab ) = (ab)
54lan 77 . . . . 5 (b ∩ (ab ) ) = (b ∩ (ab))
65ax-r4 37 . . . 4 (b ∩ (ab ) ) = (b ∩ (ab))
72, 6ax-r2 36 . . 3 (b ∪ (ab )) = (b ∩ (ab))
81, 7ax-r2 36 . 2 (a2 b) = (b ∩ (ab))
98con2 67 1 (a2 b) = (b ∩ (ab))
 Colors of variables: term Syntax hints:   = wb 1  ⊥ wn 4   ∪ wo 6   ∩ wa 7   →2 wi2 13 This theorem was proved from axioms:  ax-a1 30  ax-a2 31  ax-r1 35  ax-r2 36  ax-r4 37  ax-r5 38 This theorem depends on definitions:  df-a 40  df-i2 45 This theorem is referenced by:  wql2lem5  292  ud2lem1  563  ud2lem3  565  u2lem1  735  3vth9  812  2oalem1  825  oa43v  1028  oa63v  1032
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