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Theorem lem4.6.6i0j2 1087
Description: Equation 4.14 of [MegPav2000] p. 23. The variable i in the paper is set to 0, and j is set to 2. (Contributed by Roy F. Longton, 3-Jul-05.)
Assertion
Ref Expression
lem4.6.6i0j2 ((a ->0 b) v (a ->2 b)) = (a ->0 b)
Proof of Theorem lem4.6.6i0j2
StepHypRef Expression
1 leid 148 . . . 4 (a' v b) =< (a' v b)
2 leor 159 . . . . 5 b =< (a' v b)
3 leao1 162 . . . . 5 (a' ^ b') =< (a' v b)
42, 3lel2or 170 . . . 4 (b v (a' ^ b')) =< (a' v b)
51, 4lel2or 170 . . 3 ((a' v b) v (b v (a' ^ b'))) =< (a' v b)
6 leo 158 . . 3 (a' v b) =< ((a' v b) v (b v (a' ^ b')))
75, 6lebi 145 . 2 ((a' v b) v (b v (a' ^ b'))) = (a' v b)
8 df-i0 43 . . 3 (a ->0 b) = (a' v b)
9 df-i2 45 . . 3 (a ->2 b) = (b v (a' ^ b'))
108, 92or 72 . 2 ((a ->0 b) v (a ->2 b)) = ((a' v b) v (b v (a' ^ b')))
117, 10, 83tr1 63 1 ((a ->0 b) v (a ->2 b)) = (a ->0 b)
Colors of variables: term
Syntax hints:   = wb 1  'wn 4   v wo 6   ^ wa 7   ->0 wi0 11   ->2 wi2 13
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-i0 43  df-i2 45  df-le1 130  df-le2 131
This theorem is referenced by: (None)
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