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Theorem nom30 319
Description: Part of Lemma 3.3(14) from "Non-Orthomodular Models..." paper.
Assertion
Ref Expression
nom30 ((a ^ b) ==0 a) = (a ->1 b)
Proof of Theorem nom30
StepHypRef Expression
1 ancom 74 . . 3 (((a ^ b)' v a) ^ (a' v (a ^ b))) = ((a' v (a ^ b)) ^ ((a ^ b)' v a))
2 df-id0 49 . . 3 ((a ^ b) ==0 a) = (((a ^ b)' v a) ^ (a' v (a ^ b)))
3 df-id0 49 . . 3 (a ==0 (a ^ b)) = ((a' v (a ^ b)) ^ ((a ^ b)' v a))
41, 2, 33tr1 63 . 2 ((a ^ b) ==0 a) = (a ==0 (a ^ b))
5 nom20 313 . 2 (a ==0 (a ^ b)) = (a ->1 b)
64, 5ax-r2 36 1 ((a ^ b) ==0 a) = (a ->1 b)
Colors of variables: term
Syntax hints:   = wb 1  'wn 4   v wo 6   ^ wa 7   ->1 wi1 12   ==0 wid0 17
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-id0 49  df-le1 130  df-le2 131
This theorem is referenced by: (None)
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