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Theorem ml 1121
Description: Modular law in equational form.
Assertion
Ref Expression
ml (a v (b ^ (a v c))) = ((a v b) ^ (a v c))
Proof of Theorem ml
StepHypRef Expression
1 leo 158 . . . 4 a =< (a v b)
2 leo 158 . . . 4 a =< (a v c)
31, 2ler2an 173 . . 3 a =< ((a v b) ^ (a v c))
4 leor 159 . . . 4 b =< (a v b)
54leran 153 . . 3 (b ^ (a v c)) =< ((a v b) ^ (a v c))
63, 5lel2or 170 . 2 (a v (b ^ (a v c))) =< ((a v b) ^ (a v c))
7 ax-ml 1120 . 2 ((a v b) ^ (a v c)) =< (a v (b ^ (a v c)))
86, 7lebi 145 1 (a v (b ^ (a v c))) = ((a v b) ^ (a v c))
Colors of variables: term
Syntax hints:   = wb 1   v wo 6   ^ wa 7
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  ax-ml 1120
This theorem depends on definitions:  df-a 40  df-t 41  df-f 42  df-le1 130  df-le2 131
This theorem is referenced by:  mldual  1122  ml2i  1123  vneulem2  1130  vneulem5  1133  vneulem12  1140  vneulemexp  1146
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