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Theorem ortha 438
Description: Property of orthogonality. (Contributed by NM, 10-Mar-2002.)
Hypothesis
Ref Expression
ortha.1 ab
Assertion
Ref Expression
ortha (ab) = 0

Proof of Theorem ortha
StepHypRef Expression
1 ortha.1 . . . . 5 ab
21lecon3 157 . . . 4 ba
32lelan 167 . . 3 (ab) ≤ (aa )
4 dff 101 . . . 4 0 = (aa )
54ax-r1 35 . . 3 (aa ) = 0
63, 5lbtr 139 . 2 (ab) ≤ 0
7 le0 147 . 2 0 ≤ (ab)
86, 7lebi 145 1 (ab) = 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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