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Theorem le0 147
Description: 0 is less than or equal to anything. (Contributed by NM, 30-Aug-1997.)
Assertion
Ref Expression
le0 0 ≤ a

Proof of Theorem le0
StepHypRef Expression
1 ax-a2 31 . . 3 (0 ∪ a) = (a ∪ 0)
2 or0 102 . . 3 (a ∪ 0) = a
31, 2ax-r2 36 . 2 (0 ∪ a) = a
43df-le1 130 1 0 ≤ a
Colors of variables: term
Syntax hints:  wle 2  wo 6  0wf 9
This theorem was proved from axioms:  ax-a2 31  ax-a5 34  ax-r1 35  ax-r2 36  ax-r4 37  ax-r5 38
This theorem depends on definitions:  df-t 41  df-f 42  df-le1 130
This theorem is referenced by:  go1  343  ortha  438  ud4lem1a  577  mlalem  832  mh  879  gomaex4  900  oa3-6to3  987  oa64v  1031  vneulem7  1137  vneulemexp  1148
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