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Theorem leoa 123
Description: Relation between two methods of expressing "less than or equal to". (Contributed by NM, 11-Aug-1997.)
Hypothesis
Ref Expression
leoa.1 (ac) = b
Assertion
Ref Expression
leoa (ab) = a

Proof of Theorem leoa
StepHypRef Expression
1 leoa.1 . . . 4 (ac) = b
21ax-r1 35 . . 3 b = (ac)
32lan 77 . 2 (ab) = (a ∩ (ac))
4 anabs 121 . 2 (a ∩ (ac)) = a
53, 4ax-r2 36 1 (ab) = a
Colors of variables: term
Syntax hints:   = wb 1  wo 6  wa 7
This theorem was proved from axioms:  ax-a1 30  ax-a2 31  ax-a5 34  ax-r1 35  ax-r2 36  ax-r4 37  ax-r5 38
This theorem depends on definitions:  df-a 40
This theorem is referenced by:  df2le2  136  wlem3.1  210
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