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Theorem nom43 328
 Description: Part of Lemma 3.3(15) from "Non-Orthomodular Models..." paper. (Contributed by NM, 7-Feb-1999.)
Assertion
Ref Expression
nom43 ((ab) →3 b) = (a2 b)

Proof of Theorem nom43
StepHypRef Expression
1 ancom 74 . . . . . 6 (ba ) = (ab )
2 anor3 90 . . . . . 6 (ab ) = (ab)
31, 2ax-r2 36 . . . . 5 (ba ) = (ab)
43ud4lem0a 262 . . . 4 (b4 (ba )) = (b4 (ab) )
54ax-r1 35 . . 3 (b4 (ab) ) = (b4 (ba ))
6 nom14 311 . . 3 (b4 (ba )) = (b1 a )
75, 6ax-r2 36 . 2 (b4 (ab) ) = (b1 a )
8 i3i4 270 . 2 ((ab) →3 b) = (b4 (ab) )
9 i2i1 267 . 2 (a2 b) = (b1 a )
107, 8, 93tr1 63 1 ((ab) →3 b) = (a2 b)
 Colors of variables: term Syntax hints:   = wb 1  ⊥ wn 4   ∪ wo 6   ∩ wa 7   →1 wi1 12   →2 wi2 13   →3 wi3 14   →4 wi4 15 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-i1 44  df-i2 45  df-i3 46  df-i4 47  df-le1 130  df-le2 131 This theorem is referenced by: (None)
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