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Theorem lem4.6.6i0j4 1089
Description: Equation 4.14 of [MegPav2000] p. 23. The variable i in the paper is set to 0, and j is set to 4. (Contributed by Roy F. Longton, 3-Jul-05.)
Assertion
Ref Expression
lem4.6.6i0j4 ((a ->0 b) v (a ->4 b)) = (a ->0 b)
Proof of Theorem lem4.6.6i0j4
StepHypRef Expression
1 leid 148 . . . 4 (a' v b) =< (a' v b)
2 leao4 165 . . . . . 6 (a ^ b) =< (a' v b)
3 leao1 162 . . . . . 6 (a' ^ b) =< (a' v b)
42, 3lel2or 170 . . . . 5 ((a ^ b) v (a' ^ b)) =< (a' v b)
5 lea 160 . . . . 5 ((a' v b) ^ b') =< (a' v b)
64, 5lel2or 170 . . . 4 (((a ^ b) v (a' ^ b)) v ((a' v b) ^ b')) =< (a' v b)
71, 6lel2or 170 . . 3 ((a' v b) v (((a ^ b) v (a' ^ b)) v ((a' v b) ^ b'))) =< (a' v b)
8 leo 158 . . 3 (a' v b) =< ((a' v b) v (((a ^ b) v (a' ^ b)) v ((a' v b) ^ b')))
97, 8lebi 145 . 2 ((a' v b) v (((a ^ b) v (a' ^ b)) v ((a' v b) ^ b'))) = (a' v b)
10 df-i0 43 . . 3 (a ->0 b) = (a' v b)
11 df-i4 47 . . 3 (a ->4 b) = (((a ^ b) v (a' ^ b)) v ((a' v b) ^ b'))
1210, 112or 72 . 2 ((a ->0 b) v (a ->4 b)) = ((a' v b) v (((a ^ b) v (a' ^ b)) v ((a' v b) ^ b')))
139, 12, 103tr1 63 1 ((a ->0 b) v (a ->4 b)) = (a ->0 b)
Colors of variables: term
Syntax hints:   = wb 1  'wn 4   v wo 6   ^ wa 7   ->0 wi0 11   ->4 wi4 15
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-i4 47  df-le1 130  df-le2 131
This theorem is referenced by: (None)
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