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Theorem u3lem1n 741
 Description: Lemma for unified implication study.
Assertion
Ref Expression
u3lem1n ((a3 b) →3 a) = ((ab) ∪ (ab ))

Proof of Theorem u3lem1n
StepHypRef Expression
1 u3lem1 736 . . 3 ((a3 b) →3 a) = ((ab) ∩ (ab ))
2 ancom 74 . . . 4 ((ab) ∩ (ab )) = ((ab ) ∩ (ab))
3 df-a 40 . . . . 5 ((ab ) ∩ (ab)) = ((ab ) ∪ (ab) )
4 anor2 89 . . . . . . . 8 (ab) = (ab )
5 anor3 90 . . . . . . . 8 (ab ) = (ab)
64, 52or 72 . . . . . . 7 ((ab) ∪ (ab )) = ((ab ) ∪ (ab) )
76ax-r4 37 . . . . . 6 ((ab) ∪ (ab )) = ((ab ) ∪ (ab) )
87ax-r1 35 . . . . 5 ((ab ) ∪ (ab) ) = ((ab) ∪ (ab ))
93, 8ax-r2 36 . . . 4 ((ab ) ∩ (ab)) = ((ab) ∪ (ab ))
102, 9ax-r2 36 . . 3 ((ab) ∩ (ab )) = ((ab) ∪ (ab ))
111, 10ax-r2 36 . 2 ((a3 b) →3 a) = ((ab) ∪ (ab ))
1211con2 67 1 ((a3 b) →3 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:  u3lem2  746
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