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Theorem wbltr 397
Description: Transitive inference.
Hypotheses
Ref Expression
wbltr.1 (a == b) = 1
wbltr.2 (b =<2 c) = 1
Assertion
Ref Expression
wbltr (a =<2 c) = 1
Proof of Theorem wbltr
StepHypRef Expression
1 wbltr.1 . . . 4 (a == b) = 1
21wr5-2v 366 . . 3 ((a v c) == (b v c)) = 1
3 wbltr.2 . . . 4 (b =<2 c) = 1
43wdf-le2 379 . . 3 ((b v c) == c) = 1
52, 4wr2 371 . 2 ((a v c) == c) = 1
65wdf-le1 378 1 (a =<2 c) = 1
Colors of variables: term
Syntax hints:   = wb 1   == tb 5   v wo 6  1wt 8   =<2 wle2 10
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-wom 361
This theorem depends on definitions:  df-b 39  df-a 40  df-t 41  df-f 42  df-i1 44  df-i2 45  df-le 129  df-le1 130  df-le2 131
This theorem is referenced by:  wle3tr1  399  wledi  405  wledio  406  wlem14  430
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