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Theorem lem4.6.6i4j0 1098
Description: Equation 4.14 of [MegPav2000] p. 23. The variable i in the paper is set to 4, and j is set to 0. (Contributed by Roy F. Longton, 3-Jul-05.)
Assertion
Ref Expression
lem4.6.6i4j0 ((a ->4 b) v (a ->0 b)) = (a ->0 b)
Proof of Theorem lem4.6.6i4j0
StepHypRef Expression
1 leao4 165 . . . . 5 (a ^ b) =< (a' v b)
2 leao1 162 . . . . 5 (a' ^ b) =< (a' v b)
31, 2lel2or 170 . . . 4 ((a ^ b) v (a' ^ b)) =< (a' v b)
4 lea 160 . . . 4 ((a' v b) ^ b') =< (a' v b)
53, 4lel2or 170 . . 3 (((a ^ b) v (a' ^ b)) v ((a' v b) ^ b')) =< (a' v b)
65df-le2 131 . 2 ((((a ^ b) v (a' ^ b)) v ((a' v b) ^ b')) v (a' v b)) = (a' v b)
7 df-i4 47 . . 3 (a ->4 b) = (((a ^ b) v (a' ^ b)) v ((a' v b) ^ b'))
8 df-i0 43 . . 3 (a ->0 b) = (a' v b)
97, 82or 72 . 2 ((a ->4 b) v (a ->0 b)) = ((((a ^ b) v (a' ^ b)) v ((a' v b) ^ b')) v (a' v b))
106, 9, 83tr1 63 1 ((a ->4 b) v (a ->0 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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