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Theorem ortha 438
Description: Property of orthogonality.
Hypothesis
Ref Expression
ortha.1 a =< b'
Assertion
Ref Expression
ortha (a ^ b) = 0
Proof of Theorem ortha
StepHypRef Expression
1 ortha.1 . . . . 5 a =< b'
21lecon3 157 . . . 4 b =< a'
32lelan 167 . . 3 (a ^ b) =< (a ^ a')
4 dff 101 . . . 4 0 = (a ^ a')
54ax-r1 35 . . 3 (a ^ a') = 0
63, 5lbtr 139 . 2 (a ^ b) =< 0
7 le0 147 . 2 0 =< (a ^ b)
86, 7lebi 145 1 (a ^ b) = 0
Colors of variables: term
Syntax hints:   = wb 1   =< wle 2  'wn 4   ^ 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
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:  mhlemlem1  874  mhlem  876  e2astlem1  895  lem3.3.7i4e1  1069  lem3.3.7i5e1  1072
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