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Theorem wlebi 402
Description: L.e. to biconditional.
Hypotheses
Ref Expression
wlebi.1 (a =<2 b) = 1
wlebi.2 (b =<2 a) = 1
Assertion
Ref Expression
wlebi (a == b) = 1
Proof of Theorem wlebi
StepHypRef Expression
1 wlebi.2 . . . . 5 (b =<2 a) = 1
21wdf-le2 379 . . . 4 ((b v a) == a) = 1
32wr1 197 . . 3 (a == (b v a)) = 1
4 ax-a2 31 . . . 4 (b v a) = (a v b)
54bi1 118 . . 3 ((b v a) == (a v b)) = 1
63, 5wr2 371 . 2 (a == (a v b)) = 1
7 wlebi.1 . . 3 (a =<2 b) = 1
87wdf-le2 379 . 2 ((a v b) == b) = 1
96, 8wr2 371 1 (a == 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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