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Theorem lem4.6.6i2j1 1094
Description: Equation 4.14 of [MegPav2000] p. 23. The variable i in the paper is set to 2, and j is set to 1. (Contributed by Roy F. Longton, 3-Jul-05.)
Assertion
Ref Expression
lem4.6.6i2j1 ((a ->2 b) v (a ->1 b)) = (a ->0 b)
Proof of Theorem lem4.6.6i2j1
StepHypRef Expression
1 leor 159 . . . . 5 b =< (a' v b)
2 leao1 162 . . . . 5 (a' ^ b') =< (a' v b)
31, 2lel2or 170 . . . 4 (b v (a' ^ b')) =< (a' v b)
4 lear 161 . . . . 5 (a ^ b) =< b
54lelor 166 . . . 4 (a' v (a ^ b)) =< (a' v b)
63, 5lel2or 170 . . 3 ((b v (a' ^ b')) v (a' v (a ^ b))) =< (a' v b)
7 leo 158 . . . . 5 a' =< (a' v (a ^ b))
87lerr 150 . . . 4 a' =< ((b v (a' ^ b')) v (a' v (a ^ b)))
9 leo 158 . . . . 5 b =< (b v (a' ^ b'))
109ler 149 . . . 4 b =< ((b v (a' ^ b')) v (a' v (a ^ b)))
118, 10lel2or 170 . . 3 (a' v b) =< ((b v (a' ^ b')) v (a' v (a ^ b)))
126, 11lebi 145 . 2 ((b v (a' ^ b')) v (a' v (a ^ b))) = (a' v b)
13 df-i2 45 . . 3 (a ->2 b) = (b v (a' ^ b'))
14 df-i1 44 . . 3 (a ->1 b) = (a' v (a ^ b))
1513, 142or 72 . 2 ((a ->2 b) v (a ->1 b)) = ((b v (a' ^ b')) v (a' v (a ^ b)))
16 df-i0 43 . 2 (a ->0 b) = (a' v b)
1712, 15, 163tr1 63 1 ((a ->2 b) v (a ->1 b)) = (a ->0 b)
Colors of variables: term
Syntax hints:   = wb 1  'wn 4   v wo 6   ^ wa 7   ->0 wi0 11   ->1 wi1 12   ->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-i1 44  df-i2 45  df-le1 130  df-le2 131
This theorem is referenced by: (None)
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