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Theorem i33tr2 530
Description: Transitive inference useful for eliminating definitions.
Hypotheses
Ref Expression
i33tr2.1 (a ->3 b) = 1
i33tr2.2 a = c
i33tr2.3 b = d
Assertion
Ref Expression
i33tr2 (c ->3 d) = 1
Proof of Theorem i33tr2
StepHypRef Expression
1 i33tr2.1 . 2 (a ->3 b) = 1
2 i33tr2.2 . . 3 a = c
32ax-r1 35 . 2 c = a
4 i33tr2.3 . . 3 b = d
54ax-r1 35 . 2 d = b
61, 3, 5i33tr1 529 1 (c ->3 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: (None)
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