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Theorem binr3 519
Description: Pavicic binary logic axr3 analog.
Hypotheses
Ref Expression
binr3.1 (a ->3 c) = 1
binr3.2 (b ->3 c) = 1
Assertion
Ref Expression
binr3 ((a v b) ->3 c) = 1
Proof of Theorem binr3
StepHypRef Expression
1 binr3.1 . . . . 5 (a ->3 c) = 1
21i3le 515 . . . 4 a =< c
3 binr3.2 . . . . 5 (b ->3 c) = 1
43i3le 515 . . . 4 b =< c
52, 4le2or 168 . . 3 (a v b) =< (c v c)
6 oridm 110 . . 3 (c v c) = c
75, 6lbtr 139 . 2 (a v b) =< c
87lei3 246 1 ((a v b) ->3 c) = 1
Colors of variables: term
Syntax hints:   = wb 1   v 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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