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Theorem i3btr 528
Description: Transitive inference.
Hypotheses
Ref Expression
i3btr.1 (a ->3 b) = 1
i3btr.2 b = c
Assertion
Ref Expression
i3btr (a ->3 c) = 1
Proof of Theorem i3btr
StepHypRef Expression
1 i3btr.1 . 2 (a ->3 b) = 1
2 i3btr.2 . . . 4 b = c
32li3 252 . . 3 (a ->3 b) = (a ->3 c)
43bi1 118 . 2 ((a ->3 b) == (a ->3 c)) = 1
51, 4wwbmp 205 1 (a ->3 c) = 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:  i33tr1  529
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