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Theorem vneulem5 1133
Description: Part of von Neumann's lemma. Lemma 9, Kalmbach p. 96
Assertion
Ref Expression
vneulem5 (((x v y) v u) ^ ((x v y) v w)) = ((x v y) v (((x v y) v u) ^ w))
Proof of Theorem vneulem5
StepHypRef Expression
1 ancom 74 . 2 (((x v y) v u) ^ ((x v y) v w)) = (((x v y) v w) ^ ((x v y) v u))
2 ml 1121 . . 3 ((x v y) v (w ^ ((x v y) v u))) = (((x v y) v w) ^ ((x v y) v u))
32cm 61 . 2 (((x v y) v w) ^ ((x v y) v u)) = ((x v y) v (w ^ ((x v y) v u)))
4 ancom 74 . . 3 (w ^ ((x v y) v u)) = (((x v y) v u) ^ w)
54lor 70 . 2 ((x v y) v (w ^ ((x v y) v u))) = ((x v y) v (((x v y) v u) ^ w))
61, 3, 53tr 65 1 (((x v y) v u) ^ ((x v y) v w)) = ((x v y) v (((x v y) v u) ^ w))
Colors of variables: term
Syntax hints:   = wb 1   v wo 6   ^ wa 7
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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