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Theorem ud1lem0c 277
 Description: Lemma for unified disjunction. (Contributed by NM, 23-Nov-1997.)
Assertion
Ref Expression
ud1lem0c (a1 b) = (a ∩ (ab ))

Proof of Theorem ud1lem0c
StepHypRef Expression
1 df-i1 44 . . 3 (a1 b) = (a ∪ (ab))
2 df-a 40 . . . . . 6 (a ∩ (ab )) = (a ∪ (ab ) )
3 df-a 40 . . . . . . . . 9 (ab) = (ab )
43ax-r1 35 . . . . . . . 8 (ab ) = (ab)
54lor 70 . . . . . . 7 (a ∪ (ab ) ) = (a ∪ (ab))
65ax-r4 37 . . . . . 6 (a ∪ (ab ) ) = (a ∪ (ab))
72, 6ax-r2 36 . . . . 5 (a ∩ (ab )) = (a ∪ (ab))
87ax-r1 35 . . . 4 (a ∪ (ab)) = (a ∩ (ab ))
98con3 68 . . 3 (a ∪ (ab)) = (a ∩ (ab ))
101, 9ax-r2 36 . 2 (a1 b) = (a ∩ (ab ))
1110con2 67 1 (a1 b) = (a ∩ (ab ))
 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-r1 35  ax-r2 36  ax-r4 37  ax-r5 38 This theorem depends on definitions:  df-a 40  df-i1 44 This theorem is referenced by:  ud1lem1  560  ud1lem3  562  u1lemc6  706  u1lem11  780  i1abs  801  sa5  836  elimcons2  869  kb10iii  893
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