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Theorem wlebi 402
 Description: L.e. to biconditional.
Hypotheses
Ref Expression
wlebi.1 (a2 b) = 1
wlebi.2 (b2 a) = 1
Assertion
Ref Expression
wlebi (ab) = 1

Proof of Theorem wlebi
StepHypRef Expression
1 wlebi.2 . . . . 5 (b2 a) = 1
21wdf-le2 379 . . . 4 ((ba) ≡ a) = 1
32wr1 197 . . 3 (a ≡ (ba)) = 1
4 ax-a2 31 . . . 4 (ba) = (ab)
54bi1 118 . . 3 ((ba) ≡ (ab)) = 1
63, 5wr2 371 . 2 (a ≡ (ab)) = 1
7 wlebi.1 . . 3 (a2 b) = 1
87wdf-le2 379 . 2 ((ab) ≡ b) = 1
96, 8wr2 371 1 (ab) = 1
 Colors of variables: term Syntax hints:   = wb 1   ≡ tb 5   ∪ 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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