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Theorem wbile 401
Description: Biconditional to l.e.
Hypothesis
Ref Expression
wbile.1 (a == b) = 1
Assertion
Ref Expression
wbile (a =<2 b) = 1
Proof of Theorem wbile
StepHypRef Expression
1 wbile.1 . . . 4 (a == b) = 1
21wr5-2v 366 . . 3 ((a v b) == (b v b)) = 1
3 oridm 110 . . . 4 (b v b) = b
43bi1 118 . . 3 ((b v b) == b) = 1
52, 4wr2 371 . 2 ((a v b) == b) = 1
65wdf-le1 378 1 (a =<2 b) = 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: (None)
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