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Theorem vneulem4 1132
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
vneulem4 (((x v y) v u) ^ w) = (u ^ w)
Proof of Theorem vneulem4
StepHypRef Expression
1 vneulem1 1129 . 2 (((x v y) v u) ^ w) = (((x v y) v u) ^ ((u v w) ^ w))
2 vneulem2 1130 . 2 (((x v y) v u) ^ ((u v w) ^ w)) = ((((x v y) ^ (u v w)) v u) ^ w)
3 vneulem3.1 . . 3 ((x v y) ^ (u v w)) = 0
43vneulem3 1131 . 2 ((((x v y) ^ (u v w)) v u) ^ w) = (u ^ w)
51, 2, 43tr 65 1 (((x v y) 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-a1 30  ax-a2 31  ax-a3 32  ax-a5 34  ax-r1 35  ax-r2 36  ax-r4 37  ax-r5 38  ax-ml 1120
This theorem depends on definitions:  df-a 40  df-t 41  df-f 42  df-le1 130  df-le2 131
This theorem is referenced by:  vneulem6  1134  vneulem9  1137
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