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Theorem u4lemnaa 643
 Description: Lemma for non-tollens implication study.
Assertion
Ref Expression
u4lemnaa ((a4 b)a) = (ab )

Proof of Theorem u4lemnaa
StepHypRef Expression
1 anor2 89 . 2 ((a4 b)a) = ((a4 b) ∪ a )
2 u4lemona 628 . . . 4 ((a4 b) ∪ a ) = (ab)
32ax-r4 37 . . 3 ((a4 b) ∪ a ) = (ab)
4 anor1 88 . . . 4 (ab ) = (ab)
54ax-r1 35 . . 3 (ab) = (ab )
63, 5ax-r2 36 . 2 ((a4 b) ∪ a ) = (ab )
71, 6ax-r2 36 1 ((a4 b)a) = (ab )
 Colors of variables: term Syntax hints:   = wb 1  ⊥ wn 4   ∪ wo 6   ∩ wa 7   →4 wi4 15 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-i4 47  df-le1 130  df-le2 131  df-c1 132  df-c2 133 This theorem is referenced by:  u4lem1  737
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