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Theorem leao 124
Description: Relation between two methods of expressing "less than or equal to". (Contributed by NM, 11-Aug-1997.)
Hypothesis
Ref Expression
leao.1 (cb) = a
Assertion
Ref Expression
leao (ab) = b

Proof of Theorem leao
StepHypRef Expression
1 ax-a2 31 . . 3 (ab) = (ba)
2 leao.1 . . . . . 6 (cb) = a
32ax-r1 35 . . . . 5 a = (cb)
4 ancom 74 . . . . . 6 (bc) = (cb)
54ax-r1 35 . . . . 5 (cb) = (bc)
63, 5ax-r2 36 . . . 4 a = (bc)
76lor 70 . . 3 (ba) = (b ∪ (bc))
81, 7ax-r2 36 . 2 (ab) = (b ∪ (bc))
9 orabs 120 . 2 (b ∪ (bc)) = b
108, 9ax-r2 36 1 (ab) = b
Colors of variables: term
Syntax hints:   = wb 1  wo 6  wa 7
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-a 40
This theorem is referenced by:  df2le1  135
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