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Theorem wlecon 395
Description: Contrapositive for l.e.
Hypothesis
Ref Expression
wle.1 (a =<2 b) = 1
Assertion
Ref Expression
wlecon (b' =<2 a') = 1
Proof of Theorem wlecon
StepHypRef Expression
1 ax-a2 31 . . . . 5 (b v a) = (a v b)
21bi1 118 . . . 4 ((b v a) == (a v b)) = 1
3 oran 87 . . . . 5 (b v a) = (b' ^ a')'
43bi1 118 . . . 4 ((b v a) == (b' ^ a')') = 1
5 wle.1 . . . . 5 (a =<2 b) = 1
65wdf-le2 379 . . . 4 ((a v b) == b) = 1
72, 4, 6w3tr2 375 . . 3 ((b' ^ a')' == b) = 1
87wcon3 209 . 2 ((b' ^ a') == b') = 1
98wdf2le1 385 1 (b' =<2 a') = 1
Colors of variables: term
Syntax hints:   = wb 1  'wn 4   v wo 6   ^ wa 7  1wt 8   =<2 wle2 10
This theorem was proved from axioms:  ax-a1 30  ax-a2 31  ax-a3 32  ax-a4 33  ax-a5 34  ax-r1 35  ax-r2 36  ax-r4 37  ax-r5 38  ax-wom 361
This theorem depends on definitions:  df-b 39  df-a 40  df-t 41  df-f 42  df-i1 44  df-i2 45  df-le 129  df-le1 130  df-le2 131
This theorem is referenced by: (None)
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