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Theorem wlecon 395
 Description: Contrapositive for l.e.
Hypothesis
Ref Expression
wle.1 (a2 b) = 1
Assertion
Ref Expression
wlecon (b2 a ) = 1

Proof of Theorem wlecon
StepHypRef Expression
1 ax-a2 31 . . . . 5 (ba) = (ab)
21bi1 118 . . . 4 ((ba) ≡ (ab)) = 1
3 oran 87 . . . . 5 (ba) = (ba )
43bi1 118 . . . 4 ((ba) ≡ (ba ) ) = 1
5 wle.1 . . . . 5 (a2 b) = 1
65wdf-le2 379 . . . 4 ((ab) ≡ b) = 1
72, 4, 6w3tr2 375 . . 3 ((ba )b) = 1
87wcon3 209 . 2 ((ba ) ≡ b ) = 1
98wdf2le1 385 1 (b2 a ) = 1
 Colors of variables: term Syntax hints:   = wb 1  ⊥ wn 4   ∪ 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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