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Theorem ler2or 172
Description: Disjunction of 2 l.e.'s.
Hypotheses
Ref Expression
ler2.1 a =< b
ler2.2 a =< c
Assertion
Ref Expression
ler2or a =< (b v c)
Proof of Theorem ler2or
StepHypRef Expression
1 oridm 110 . . 3 (a v a) = a
21ax-r1 35 . 2 a = (a v a)
3 ler2.1 . . 3 a =< b
4 ler2.2 . . 3 a =< c
53, 4le2or 168 . 2 (a v a) =< (b v c)
62, 5bltr 138 1 a =< (b v c)
Colors of variables: term
Syntax hints:   =< wle 2   v wo 6
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-le1 130  df-le2 131
This theorem is referenced by:  distid  887
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