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Theorem u2lemob 631
 Description: Lemma for Dishkant implication study. (Contributed by NM, 15-Dec-1997.)
Assertion
Ref Expression
u2lemob ((a2 b) ∪ b) = ((ab ) ∪ b)

Proof of Theorem u2lemob
StepHypRef Expression
1 df-i2 45 . . 3 (a2 b) = (b ∪ (ab ))
21ax-r5 38 . 2 ((a2 b) ∪ b) = ((b ∪ (ab )) ∪ b)
3 or32 82 . . 3 ((b ∪ (ab )) ∪ b) = ((bb) ∪ (ab ))
4 ax-a2 31 . . . 4 ((bb) ∪ (ab )) = ((ab ) ∪ (bb))
5 oridm 110 . . . . 5 (bb) = b
65lor 70 . . . 4 ((ab ) ∪ (bb)) = ((ab ) ∪ b)
74, 6ax-r2 36 . . 3 ((bb) ∪ (ab )) = ((ab ) ∪ b)
83, 7ax-r2 36 . 2 ((b ∪ (ab )) ∪ b) = ((ab ) ∪ b)
92, 8ax-r2 36 1 ((a2 b) ∪ b) = ((ab ) ∪ b)
 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-a3 32  ax-a5 34  ax-r1 35  ax-r2 36  ax-r4 37  ax-r5 38 This theorem depends on definitions:  df-t 41  df-f 42  df-i2 45 This theorem is referenced by:  u2lemnanb  656
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