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Theorem vneulem8 1136
Description: Part of von Neumann's lemma. Lemma 9, Kalmbach p. 96
Hypothesis
Ref Expression
vneulem6.1 ((a v b) ^ (c v d)) = 0
Assertion
Ref Expression
vneulem8 (((a v b) v d) ^ ((b v c) v d)) = (b v d)
Proof of Theorem vneulem8
StepHypRef Expression
1 vneulem6.1 . . 3 ((a v b) ^ (c v d)) = 0
21vneulem6 1134 . 2 (((a v b) v d) ^ ((b v c) v d)) = ((c ^ a) v (b v d))
31vneulem7 1135 . 2 ((c ^ a) v (b v d)) = (b v d)
42, 3tr 62 1 (((a v b) v d) ^ ((b v c) v d)) = (b v d)
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:  vneulem10  1138  vneulem15  1143
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