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Theorem vneulem3 1131
Description: Part of von Neumann's lemma. Lemma 9, Kalmbach p. 96
Hypothesis
Ref Expression
vneulem3.1 ((x v y) ^ (u v w)) = 0
Assertion
Ref Expression
vneulem3 ((((x v y) ^ (u v w)) v u) ^ w) = (u ^ w)
Proof of Theorem vneulem3
StepHypRef Expression
1 vneulem3.1 . . . 4 ((x v y) ^ (u v w)) = 0
21ror 71 . . 3 (((x v y) ^ (u v w)) v u) = (0 v u)
3 or0r 103 . . 3 (0 v u) = u
42, 3tr 62 . 2 (((x v y) ^ (u v w)) v u) = u
54ran 78 1 ((((x v y) ^ (u v w)) v u) ^ w) = (u ^ w)
Colors of variables: term
Syntax hints:   = wb 1   v wo 6   ^ wa 7  0wf 9
This theorem was proved from axioms:  ax-a2 31  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
This theorem is referenced by:  vneulem4  1132
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