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Theorem leao 124
Description: Relation between two methods of expressing "less than or equal to".
Hypothesis
Ref Expression
leao.1 (c ^ b) = a
Assertion
Ref Expression
leao (a v b) = b
Proof of Theorem leao
StepHypRef Expression
1 ax-a2 31 . . 3 (a v b) = (b v a)
2 leao.1 . . . . . 6 (c ^ b) = a
32ax-r1 35 . . . . 5 a = (c ^ b)
4 ancom 74 . . . . . 6 (b ^ c) = (c ^ b)
54ax-r1 35 . . . . 5 (c ^ b) = (b ^ c)
63, 5ax-r2 36 . . . 4 a = (b ^ c)
76lor 70 . . 3 (b v a) = (b v (b ^ c))
81, 7ax-r2 36 . 2 (a v b) = (b v (b ^ c))
9 orabs 120 . 2 (b v (b ^ c)) = b
108, 9ax-r2 36 1 (a v b) = b
Colors of variables: term
Syntax hints:   = wb 1   v 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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