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Theorem i33tr1 529
Description: Transitive inference useful for introducing definitions. (Contributed by NM, 7-Nov-1997.)
Hypotheses
Ref Expression
i33tr1.1 (a3 b) = 1
i33tr1.2 c = a
i33tr1.3 d = b
Assertion
Ref Expression
i33tr1 (c3 d) = 1

Proof of Theorem i33tr1
StepHypRef Expression
1 i33tr1.2 . . 3 c = a
2 i33tr1.1 . . 3 (a3 b) = 1
31, 2bi3tr 527 . 2 (c3 b) = 1
4 i33tr1.3 . . 3 d = b
54ax-r1 35 . 2 b = d
63, 5i3btr 528 1 (c3 d) = 1
Colors of variables: term
Syntax hints:   = wb 1  1wt 8  3 wi3 14
This theorem was proved from axioms:  ax-a1 30  ax-a2 31  ax-a4 33  ax-a5 34  ax-r1 35  ax-r2 36  ax-r4 37  ax-r5 38
This theorem depends on definitions:  df-b 39  df-a 40  df-t 41  df-f 42  df-i3 46
This theorem is referenced by:  i33tr2  530  i3con1  531  i3ran  535  i3lan  536
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