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Theorem i3con1 531
Description: Contrapositive. (Contributed by NM, 7-Nov-1997.)
Hypothesis
Ref Expression
i3con1.1 (a3 b ) = 1
Assertion
Ref Expression
i3con1 (b3 a) = 1

Proof of Theorem i3con1
StepHypRef Expression
1 i3con1.1 . . 3 (a3 b ) = 1
21binr1 517 . 2 (b 3 a ) = 1
3 ax-a1 30 . 2 b = b
4 ax-a1 30 . 2 a = a
52, 3, 4i33tr1 529 1 (b3 a) = 1
Colors of variables: term
Syntax hints:   = wb 1   wn 4  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: (None)
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