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Theorem u1lem9a 777
Description: Lemma used in study of orthoarguesian law. Equation 4.11 of [MegPav2000] p. 23. This is the first part of the inequality.
Assertion
Ref Expression
u1lem9a (a' ->1 b)' =< a'
Proof of Theorem u1lem9a
StepHypRef Expression
1 df-i1 44 . . . 4 (a' ->1 b) = (a'' v (a' ^ b))
21ax-r4 37 . . 3 (a' ->1 b)' = (a'' v (a' ^ b))'
3 anor1 88 . . . 4 (a' ^ (a' ^ b)') = (a'' v (a' ^ b))'
43ax-r1 35 . . 3 (a'' v (a' ^ b))' = (a' ^ (a' ^ b)')
52, 4ax-r2 36 . 2 (a' ->1 b)' = (a' ^ (a' ^ b)')
6 lea 160 . 2 (a' ^ (a' ^ b)') =< a'
75, 6bltr 138 1 (a' ->1 b)' =< a'
Colors of variables: term
Syntax hints:   =< wle 2  'wn 4   v wo 6   ^ wa 7   ->1 wi1 12
This theorem was proved from axioms:  ax-a1 30  ax-a2 31  ax-a5 34  ax-r1 35  ax-r2 36  ax-r4 37  ax-r5 38
This theorem depends on definitions:  df-a 40  df-i1 44  df-le1 130  df-le2 131
This theorem is referenced by:  u1lem9ab  779  sadm3  838  oa4uto4g  975  oa4uto4  977  lem4.6.3le1  1082
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