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Theorem u5lemnaa 644
 Description: Lemma for relevance implication study. (Contributed by NM, 15-Dec-1997.)
Assertion
Ref Expression
u5lemnaa ((a5 b)a) = (a ∩ (ab ))

Proof of Theorem u5lemnaa
StepHypRef Expression
1 anor2 89 . 2 ((a5 b)a) = ((a5 b) ∪ a )
2 u5lemona 629 . . . 4 ((a5 b) ∪ a ) = (a ∪ (ab))
32ax-r4 37 . . 3 ((a5 b) ∪ a ) = (a ∪ (ab))
4 anor1 88 . . . . 5 (a ∩ (ab) ) = (a ∪ (ab))
54ax-r1 35 . . . 4 (a ∪ (ab)) = (a ∩ (ab) )
6 df-a 40 . . . . . 6 (ab) = (ab )
76con2 67 . . . . 5 (ab) = (ab )
87lan 77 . . . 4 (a ∩ (ab) ) = (a ∩ (ab ))
95, 8ax-r2 36 . . 3 (a ∪ (ab)) = (a ∩ (ab ))
103, 9ax-r2 36 . 2 ((a5 b) ∪ a ) = (a ∩ (ab ))
111, 10ax-r2 36 1 ((a5 b)a) = (a ∩ (ab ))
 Colors of variables: term Syntax hints:   = wb 1  ⊥ wn 4   ∪ wo 6   ∩ wa 7   →5 wi5 16 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-a 40  df-t 41  df-f 42  df-i5 48  df-le1 130  df-le2 131 This theorem is referenced by: (None)
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