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Theorem binr3 519
 Description: Pavicic binary logic axr3 analog.
Hypotheses
Ref Expression
binr3.1 (a3 c) = 1
binr3.2 (b3 c) = 1
Assertion
Ref Expression
binr3 ((ab) →3 c) = 1

Proof of Theorem binr3
StepHypRef Expression
1 binr3.1 . . . . 5 (a3 c) = 1
21i3le 515 . . . 4 ac
3 binr3.2 . . . . 5 (b3 c) = 1
43i3le 515 . . . 4 bc
52, 4le2or 168 . . 3 (ab) ≤ (cc)
6 oridm 110 . . 3 (cc) = c
75, 6lbtr 139 . 2 (ab) ≤ c
87lei3 246 1 ((ab) →3 c) = 1
 Colors of variables: term Syntax hints:   = wb 1   ∪ wo 6  1wt 8   →3 wi3 14 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-r3 439 This theorem depends on definitions:  df-b 39  df-a 40  df-t 41  df-f 42  df-i3 46  df-le1 130  df-le2 131  df-c1 132  df-c2 133 This theorem is referenced by:  i3ror  532
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