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Theorem oagen2b 1017
Description: "Generalized" OA.
Hypotheses
Ref Expression
oagen2b.1 d =< (a ->2 b)
oagen2b.2 e =< ((b v c) ->0 ((a ->2 b) ^ (a ->2 c)))
Assertion
Ref Expression
oagen2b (d ^ e) =< (a ->2 c)
Proof of Theorem oagen2b
StepHypRef Expression
1 oagen2b.1 . . 3 d =< (a ->2 b)
21leran 153 . 2 (d ^ e) =< ((a ->2 b) ^ e)
3 oagen2b.2 . . 3 e =< ((b v c) ->0 ((a ->2 b) ^ (a ->2 c)))
43oagen2 1016 . 2 ((a ->2 b) ^ e) =< (a ->2 c)
52, 4letr 137 1 (d ^ e) =< (a ->2 c)
Colors of variables: term
Syntax hints:   =< wle 2   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  ax-3oa 998
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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